diff --git a/DifferentiationInterface/CHANGELOG.md b/DifferentiationInterface/CHANGELOG.md
index e75526fbf..575d9cff7 100644
--- a/DifferentiationInterface/CHANGELOG.md
+++ b/DifferentiationInterface/CHANGELOG.md
@@ -7,6 +7,14 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased](https://github.com/JuliaDiff/DifferentiationInterface.jl/compare/DifferentiationInterface-v0.7.21...main)
 
+### Added
+
+- New operators `value_gradient_and_hvp` and `value_gradient_and_hvp!`, which also return the primal value ([#1086](https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/1086))
+
+### Deprecated
+
+- `gradient_and_hvp` and `gradient_and_hvp!` are deprecated in favor of `value_gradient_and_hvp` and `value_gradient_and_hvp!` ([#1086](https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/1086))
+
 ### Fixed
 
 - Speed up `pick_batchsize` when the batch size is only known at run time ([#1076](https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/1076))
diff --git a/DifferentiationInterface/Project.toml b/DifferentiationInterface/Project.toml
index a2a694816..594a3f743 100644
--- a/DifferentiationInterface/Project.toml
+++ b/DifferentiationInterface/Project.toml
@@ -1,6 +1,6 @@
 name = "DifferentiationInterface"
 uuid = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
-version = "0.7.21"
+version = "0.7.22"
 authors = ["Guillaume Dalle", "Adrian Hill"]
 
 [deps]
diff --git a/DifferentiationInterface/docs/src/api.md b/DifferentiationInterface/docs/src/api.md
index eba5cee96..931566fa0 100644
--- a/DifferentiationInterface/docs/src/api.md
+++ b/DifferentiationInterface/docs/src/api.md
@@ -94,6 +94,8 @@ prepare_hvp
 prepare_hvp_same_point
 hvp
 hvp!
+value_gradient_and_hvp
+value_gradient_and_hvp!
 gradient_and_hvp
 gradient_and_hvp!
 ```
diff --git a/DifferentiationInterface/docs/src/explanation/operators.md b/DifferentiationInterface/docs/src/explanation/operators.md
index 9664a03a4..ec5d9efa6 100644
--- a/DifferentiationInterface/docs/src/explanation/operators.md
+++ b/DifferentiationInterface/docs/src/explanation/operators.md
@@ -60,7 +60,7 @@ Several variants of each operator are defined:
 | [`jacobian`](@ref)          | [`jacobian!`](@ref)          | [`value_and_jacobian`](@ref)                     | [`value_and_jacobian!`](@ref)                     |
 | [`pushforward`](@ref)       | [`pushforward!`](@ref)       | [`value_and_pushforward`](@ref)                  | [`value_and_pushforward!`](@ref)                  |
 | [`pullback`](@ref)          | [`pullback!`](@ref)          | [`value_and_pullback`](@ref)                     | [`value_and_pullback!`](@ref)                     |
-| [`hvp`](@ref)               | [`hvp!`](@ref)               | [`gradient_and_hvp`](@ref)                       | [`gradient_and_hvp!`](@ref)                       |
+| [`hvp`](@ref)               | [`hvp!`](@ref)               | [`value_gradient_and_hvp`](@ref)                 | [`value_gradient_and_hvp!`](@ref)                 |
 
 ## Mutation and signatures
 
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceFastDifferentiationExt/onearg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceFastDifferentiationExt/onearg.jl
index 316d1611c..5c6edfb6d 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceFastDifferentiationExt/onearg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceFastDifferentiationExt/onearg.jl
@@ -599,7 +599,7 @@ function DI.hvp!(
     return tg
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f,
         prep::FastDifferentiationHVPPrep,
         backend::AutoFastDifferentiation,
@@ -609,11 +609,11 @@ function DI.gradient_and_hvp(
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     tg = DI.hvp(f, prep, backend, x, tx, contexts...)
-    grad = DI.gradient(f, prep.gradient_prep, backend, x, contexts...)
-    return grad, tg
+    y, grad = DI.value_and_gradient(f, prep.gradient_prep, backend, x, contexts...)
+    return y, grad, tg
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f,
         grad,
         tg::NTuple,
@@ -625,8 +625,8 @@ function DI.gradient_and_hvp!(
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     DI.hvp!(f, tg, prep, backend, x, tx, contexts...)
-    DI.gradient!(f, grad, prep.gradient_prep, backend, x, contexts...)
-    return grad, tg
+    y, _ = DI.value_and_gradient!(f, grad, prep.gradient_prep, backend, x, contexts...)
+    return y, grad, tg
 end
 
 ## Hessian
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceGTPSAExt/onearg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceGTPSAExt/onearg.jl
index d39f4747e..1d8ce650e 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceGTPSAExt/onearg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceGTPSAExt/onearg.jl
@@ -609,7 +609,7 @@ function DI.hvp!(
     return tg
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f,
         prep::GTPSAOneArgHVPPrep,
         backend::AutoGTPSA{D},
@@ -619,7 +619,7 @@ function DI.gradient_and_hvp(
     ) where {D, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     grad = similar(x, eltype(prep.hess))
-    DI.value_gradient_and_hessian!(
+    y, _, _ = DI.value_gradient_and_hessian!(
         f, grad, prep.hess, prep.hessprep, backend, x, contexts...
     )
     tg = map(tx) do dx
@@ -634,10 +634,10 @@ function DI.gradient_and_hvp(
         end
         return dg
     end
-    return grad, tg
+    return y, grad, tg
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f,
         grad,
         tg,
@@ -648,7 +648,7 @@ function DI.gradient_and_hvp!(
         contexts::Vararg{DI.Constant, C},
     ) where {D, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    DI.value_gradient_and_hessian!(
+    y, _, _ = DI.value_gradient_and_hessian!(
         f, grad, prep.hess, prep.hessprep, backend, x, contexts...
     )
     for b in eachindex(tg, tx)
@@ -662,5 +662,5 @@ function DI.gradient_and_hvp!(
             j += 1
         end
     end
-    return grad, tg
+    return y, grad, tg
 end
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceHyperHessiansExt/DifferentiationInterfaceHyperHessiansExt.jl b/DifferentiationInterface/ext/DifferentiationInterfaceHyperHessiansExt/DifferentiationInterfaceHyperHessiansExt.jl
index b6426527f..ae8fd18f2 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceHyperHessiansExt/DifferentiationInterfaceHyperHessiansExt.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceHyperHessiansExt/DifferentiationInterfaceHyperHessiansExt.jl
@@ -283,7 +283,7 @@ function DI.hvp!(
     return hvp!(tg, fc, x, tx, prep.cfg)
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f,
         prep::HyperHessiansHVPPrep,
         backend::DI.AutoHyperHessians,
@@ -295,10 +295,10 @@ function DI.gradient_and_hvp(
     contexts_prepared = translate_prepared(contexts, prep.contexts_prepared)
     fc = DI.fix_tail(f, contexts_prepared...)
     res = hvp_gradient_value(fc, x, tx, prep.cfg)
-    return res.gradient, res.hvp
+    return res.value, res.gradient, res.hvp
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f,
         grad,
         tg::NTuple,
@@ -311,8 +311,8 @@ function DI.gradient_and_hvp!(
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     contexts_prepared = translate_prepared(contexts, prep.contexts_prepared)
     fc = DI.fix_tail(f, contexts_prepared...)
-    hvp_gradient_value!(tg, grad, fc, x, tx, prep.cfg)
-    return grad, tg
+    y = hvp_gradient_value!(tg, grad, fc, x, tx, prep.cfg)
+    return y, grad, tg
 end
 
 end
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/second_order.jl b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/second_order.jl
index 942267727..0b9063968 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/second_order.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceMooncakeExt/second_order.jl
@@ -13,7 +13,7 @@ function DI.prepare_hvp_nokwarg(
     return prep
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f::F,
         prep::MooncakeHVPPrep{Y},
         backend::AutoMooncakeForwardOverReverse,
@@ -24,19 +24,19 @@ function DI.gradient_and_hvp(
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     dx = only(tx)
     if isempty(contexts)
-        _, new_g, new_dg = value_and_hvp!!(
+        y, new_g, new_dg = value_and_hvp!!(
             prep.cache, f, (dx,), x
         )
     else
         dall = (dx, map(zero_tangent_unwrap, contexts)...)
-        _, (new_g,), (new_dg,) = value_and_hvp!!(
+        y, (new_g,), (new_dg,) = value_and_hvp!!(
             prep.cache, f, dall, x, map(DI.unwrap, contexts)...
         )
     end
-    return _copy_output(new_g), (_copy_output(new_dg),)
+    return y, _copy_output(new_g), (_copy_output(new_dg),)
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f::F,
         prep::MooncakeHVPPrep{Y},
         backend::AutoMooncakeForwardOverReverse,
@@ -45,25 +45,25 @@ function DI.gradient_and_hvp(
         contexts::Vararg{DI.Context, C},
     ) where {F, Y, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    gs_and_tg = map(tx) do dx
+    ys_gs_and_tg = map(tx) do dx
         if isempty(contexts)
-            _, new_g, new_dg = value_and_hvp!!(
+            y, new_g, new_dg = value_and_hvp!!(
                 prep.cache, f, dx, x
             )
         else
             dall = (dx, map(zero_tangent_unwrap, contexts)...)
-            _, (new_g,), (new_dg,) = value_and_hvp!!(
+            y, (new_g,), (new_dg,) = value_and_hvp!!(
                 prep.cache, f, dall, x, map(DI.unwrap, contexts)...
             )
         end
-        _copy_output(new_g), _copy_output(new_dg)
+        y, _copy_output(new_g), _copy_output(new_dg)
     end
-    g = first(gs_and_tg[1])
-    tg = map(last, gs_and_tg)
-    return g, tg
+    y, g, _ = ys_gs_and_tg[1]
+    tg = map(last, ys_gs_and_tg)
+    return y, g, tg
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f::F,
         g,
         tg::NTuple,
@@ -74,10 +74,10 @@ function DI.gradient_and_hvp!(
         contexts::Vararg{DI.Context, C},
     ) where {F, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    new_g, new_tg = DI.gradient_and_hvp(f, prep, backend, x, tx, contexts...)
+    y, new_g, new_tg = DI.value_gradient_and_hvp(f, prep, backend, x, tx, contexts...)
     copyto!(g, new_g)
     foreach(copyto!, tg, new_tg)
-    return g, tg
+    return y, g, tg
 end
 
 function DI.hvp(
@@ -89,7 +89,7 @@ function DI.hvp(
         contexts::Vararg{DI.Context, C},
     ) where {F, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    return DI.gradient_and_hvp(f, prep, backend, x, tx, contexts...)[2]
+    return DI.value_gradient_and_hvp(f, prep, backend, x, tx, contexts...)[3]
 end
 
 function DI.hvp!(
@@ -102,7 +102,7 @@ function DI.hvp!(
         contexts::Vararg{DI.Context, C},
     ) where {F, C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    _, new_tg = DI.gradient_and_hvp(f, prep, backend, x, tx, contexts...)
+    _, _, new_tg = DI.value_gradient_and_hvp(f, prep, backend, x, tx, contexts...)
     foreach(copyto!, tg, new_tg)
     return tg
 end
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceSymbolicsExt/onearg.jl b/DifferentiationInterface/ext/DifferentiationInterfaceSymbolicsExt/onearg.jl
index 94079fcce..c0e8f361f 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceSymbolicsExt/onearg.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceSymbolicsExt/onearg.jl
@@ -483,7 +483,7 @@ function DI.hvp!(
     return tg
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f,
         prep::SymbolicsOneArgHVPPrep,
         backend::AutoSymbolics,
@@ -493,11 +493,11 @@ function DI.gradient_and_hvp(
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     tg = DI.hvp(f, prep, backend, x, tx, contexts...)
-    grad = DI.gradient(f, prep.gradient_prep, backend, x, contexts...)
-    return grad, tg
+    y, grad = DI.value_and_gradient(f, prep.gradient_prep, backend, x, contexts...)
+    return y, grad, tg
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f,
         grad,
         tg::NTuple,
@@ -509,8 +509,8 @@ function DI.gradient_and_hvp!(
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
     DI.hvp!(f, tg, prep, backend, x, tx, contexts...)
-    DI.gradient!(f, grad, prep.gradient_prep, backend, x, contexts...)
-    return grad, tg
+    y, _ = DI.value_and_gradient!(f, grad, prep.gradient_prep, backend, x, contexts...)
+    return y, grad, tg
 end
 
 ## Second derivative
diff --git a/DifferentiationInterface/ext/DifferentiationInterfaceZygoteExt/DifferentiationInterfaceZygoteExt.jl b/DifferentiationInterface/ext/DifferentiationInterfaceZygoteExt/DifferentiationInterfaceZygoteExt.jl
index cf2a0820b..852572f14 100644
--- a/DifferentiationInterface/ext/DifferentiationInterfaceZygoteExt/DifferentiationInterfaceZygoteExt.jl
+++ b/DifferentiationInterface/ext/DifferentiationInterfaceZygoteExt/DifferentiationInterfaceZygoteExt.jl
@@ -229,7 +229,7 @@ function DI.hvp!(
     )
 end
 
-function DI.gradient_and_hvp(
+function DI.value_gradient_and_hvp(
         f,
         prep::ZygoteHVPPrep,
         backend::AutoZygote,
@@ -238,12 +238,12 @@ function DI.gradient_and_hvp(
         contexts::Vararg{DI.Context, C},
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    return DI.gradient_and_hvp(
+    return DI.value_gradient_and_hvp(
         f, prep.fd_prep, DI.SecondOrder(AutoForwardDiff(), backend), x, tx, contexts...
     )
 end
 
-function DI.gradient_and_hvp!(
+function DI.value_gradient_and_hvp!(
         f,
         grad,
         tg::NTuple,
@@ -254,7 +254,7 @@ function DI.gradient_and_hvp!(
         contexts::Vararg{DI.Context, C},
     ) where {C}
     DI.check_prep(f, prep, backend, x, tx, contexts...)
-    return DI.gradient_and_hvp!(
+    return DI.value_gradient_and_hvp!(
         f,
         grad,
         tg,
diff --git a/DifferentiationInterface/src/DifferentiationInterface.jl b/DifferentiationInterface/src/DifferentiationInterface.jl
index 6f60b65df..6fc7f7e3b 100644
--- a/DifferentiationInterface/src/DifferentiationInterface.jl
+++ b/DifferentiationInterface/src/DifferentiationInterface.jl
@@ -92,7 +92,8 @@ export jacobian!, jacobian
 
 export second_derivative!, second_derivative
 export value_derivative_and_second_derivative, value_derivative_and_second_derivative!
-export hvp!, hvp, gradient_and_hvp, gradient_and_hvp!
+export hvp!, hvp, value_gradient_and_hvp, value_gradient_and_hvp!
+export gradient_and_hvp, gradient_and_hvp!
 export hessian!, hessian
 export value_gradient_and_hessian, value_gradient_and_hessian!
 
diff --git a/DifferentiationInterface/src/second_order/hvp.jl b/DifferentiationInterface/src/second_order/hvp.jl
index 068781727..0e4cd4f7e 100644
--- a/DifferentiationInterface/src/second_order/hvp.jl
+++ b/DifferentiationInterface/src/second_order/hvp.jl
@@ -90,31 +90,65 @@ function hvp!(
 end
 
 """
-    gradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)
+    value_gradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (y, grad, tg)
 
-Compute the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`.
+Compute the value, the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`.
 
 $(docstring_preparation_hint("hvp"; same_point = true))
 """
-function gradient_and_hvp(
+function value_gradient_and_hvp(
         f::F, backend::AbstractADType, x, tx, contexts::Vararg{Context, C}
     ) where {F, C}
     prep = prepare_hvp_nokwarg(Val(true), f, backend, x, tx, contexts...)
-    return gradient_and_hvp(f, prep, backend, x, tx, contexts...)
+    return value_gradient_and_hvp(f, prep, backend, x, tx, contexts...)
 end
 
 """
-    gradient_and_hvp!(f, grad, tg, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)
+    value_gradient_and_hvp!(f, grad, tg, [prep,] backend, x, tx, [contexts...]) -> (y, grad, tg)
 
-Compute the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`, overwriting `grad` and `tg`.
+Compute the value, the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`, overwriting `grad` and `tg`.
 
 $(docstring_preparation_hint("hvp"; same_point = true))
 """
-function gradient_and_hvp!(
+function value_gradient_and_hvp!(
         f::F, grad, tg, backend::AbstractADType, x, tx, contexts::Vararg{Context, C}
     ) where {F, C}
     prep = prepare_hvp_nokwarg(Val(true), f, backend, x, tx, contexts...)
-    return gradient_and_hvp!(f, grad, tg, prep, backend, x, tx, contexts...)
+    return value_gradient_and_hvp!(f, grad, tg, prep, backend, x, tx, contexts...)
+end
+
+"""
+    gradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)
+
+Compute the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`.
+
+!!! warning "Deprecated"
+
+    Use [`value_gradient_and_hvp`](@ref) instead.
+"""
+function gradient_and_hvp(f::F, args::Vararg{Any, N}) where {F, N}
+    Base.depwarn(
+        "`gradient_and_hvp` is deprecated, use `value_gradient_and_hvp` instead.",
+        :gradient_and_hvp,
+    )
+    return Base.tail(value_gradient_and_hvp(f, args...))
+end
+
+"""
+    gradient_and_hvp!(f, grad, tg, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)
+
+Compute the gradient and the Hessian-vector product of `f` at point `x` with a tuple of tangents `tx`, overwriting `grad` and `tg`.
+
+!!! warning "Deprecated"
+
+    Use [`value_gradient_and_hvp!`](@ref) instead.
+"""
+function gradient_and_hvp!(f::F, args::Vararg{Any, N}) where {F, N}
+    Base.depwarn(
+        "`gradient_and_hvp!` is deprecated, use `value_gradient_and_hvp!` instead.",
+        :gradient_and_hvp!,
+    )
+    return Base.tail(value_gradient_and_hvp!(f, args...))
 end
 
 ## Preparation
@@ -409,7 +443,7 @@ function _hvp_aux!(
     )
 end
 
-function gradient_and_hvp(
+function value_gradient_and_hvp(
         f::F,
         prep::ForwardOverAnythingHVPPrep,
         backend::AbstractADType,
@@ -427,12 +461,14 @@ function gradient_and_hvp(
         Constant(rewrap),
         contexts...,
     )
-    return value_and_pushforward(
+    y = f(x, map(unwrap, contexts)...)
+    grad, tg = value_and_pushforward(
         shuffled_gradient, outer_pushforward_prep, outer(backend), x, tx, new_contexts...
     )
+    return y, grad, tg
 end
 
-function gradient_and_hvp!(
+function value_gradient_and_hvp!(
         f::F,
         grad,
         tg::NTuple,
@@ -443,9 +479,11 @@ function gradient_and_hvp!(
         contexts::Vararg{Context, C},
     ) where {F, C}
     check_prep(f, prep, backend, x, tx, contexts...)
-    return _gradient_and_hvp_aux!(
+    y = f(x, map(unwrap, contexts)...)
+    _gradient_and_hvp_aux!(
         inplace_support(outer(backend)), f, grad, tg, prep, backend, x, tx, contexts...
     )
+    return y, grad, tg
 end
 
 function _gradient_and_hvp_aux!(
@@ -604,7 +642,7 @@ function hvp!(
     return tg
 end
 
-function gradient_and_hvp(
+function value_gradient_and_hvp(
         f::F,
         prep::ReverseOverForwardHVPPrep,
         backend::AbstractADType,
@@ -614,11 +652,11 @@ function gradient_and_hvp(
     ) where {F, C}
     check_prep(f, prep, backend, x, tx, contexts...)
     tg = hvp(f, prep, backend, x, tx, contexts...)
-    grad = gradient(f, prep.gradient_prep, inner(backend), x, contexts...)
-    return grad, tg
+    y, grad = value_and_gradient(f, prep.gradient_prep, inner(backend), x, contexts...)
+    return y, grad, tg
 end
 
-function gradient_and_hvp!(
+function value_gradient_and_hvp!(
         f::F,
         grad,
         tg::NTuple,
@@ -630,8 +668,8 @@ function gradient_and_hvp!(
     ) where {F, C}
     check_prep(f, prep, backend, x, tx, contexts...)
     hvp!(f, tg, prep, backend, x, tx, contexts...)
-    gradient!(f, grad, prep.gradient_prep, inner(backend), x, contexts...)
-    return grad, tg
+    y, _ = value_and_gradient!(f, grad, prep.gradient_prep, inner(backend), x, contexts...)
+    return y, grad, tg
 end
 
 ## Reverse over reverse
@@ -762,7 +800,7 @@ function _hvp_aux!(
     )
 end
 
-function gradient_and_hvp(
+function value_gradient_and_hvp(
         f::F,
         prep::ReverseOverReverseHVPPrep,
         backend::AbstractADType,
@@ -776,12 +814,14 @@ function gradient_and_hvp(
     new_contexts = (
         FunctionContext(f), Constant(inner(backend)), Constant(rewrap), contexts...,
     )
-    return value_and_pullback(
+    y = f(x, map(unwrap, contexts)...)
+    grad, tg = value_and_pullback(
         shuffled_gradient, outer_pullback_prep, outer(backend), x, tx, new_contexts...
     )
+    return y, grad, tg
 end
 
-function gradient_and_hvp!(
+function value_gradient_and_hvp!(
         f::F,
         grad,
         tg::NTuple,
@@ -792,9 +832,11 @@ function gradient_and_hvp!(
         contexts::Vararg{Context, C},
     ) where {F, C}
     check_prep(f, prep, backend, x, tx, contexts...)
-    return _gradient_and_hvp_aux!(
+    y = f(x, map(unwrap, contexts)...)
+    _gradient_and_hvp_aux!(
         inplace_support(outer(backend)), f, grad, tg, prep, backend, x, tx, contexts...
     )
+    return y, grad, tg
 end
 
 function _gradient_and_hvp_aux!(
diff --git a/DifferentiationInterface/test/Core/Internals/deprecations.jl b/DifferentiationInterface/test/Core/Internals/deprecations.jl
new file mode 100644
index 000000000..7bee804a1
--- /dev/null
+++ b/DifferentiationInterface/test/Core/Internals/deprecations.jl
@@ -0,0 +1,29 @@
+using DifferentiationInterface
+using DifferentiationInterface: AutoSimpleFiniteDiff
+using Test
+
+@testset "gradient_and_hvp is deprecated" begin
+    f(x) = sum(abs2, x)
+    backend = AutoSimpleFiniteDiff()
+    x = [1.0, 2.0]
+    tx = ([1.0, 0.0], [0.0, 1.0])
+    prep = prepare_hvp(f, backend, x, tx)
+
+    y, grad, tg = value_gradient_and_hvp(f, prep, backend, x, tx)
+    @test y ≈ 5
+    @test grad ≈ [2, 4]
+    @test all(isapprox.(tg, ([2, 0], [0, 2]); rtol = 1.0e-3))
+
+    grad_dep, tg_dep = @test_deprecated gradient_and_hvp(f, prep, backend, x, tx)
+    @test grad_dep ≈ grad
+    @test all(tg_dep .≈ tg)
+
+    grad_in, tg_in = similar(x), map(similar, tx)
+    grad_dep!, tg_dep! = @test_deprecated gradient_and_hvp!(
+        f, grad_in, tg_in, prep, backend, x, tx
+    )
+    @test grad_dep! === grad_in
+    @test tg_dep! === tg_in
+    @test grad_dep! ≈ grad
+    @test all(tg_dep! .≈ tg)
+end
diff --git a/DifferentiationInterfaceTest/CHANGELOG.md b/DifferentiationInterfaceTest/CHANGELOG.md
index 46857eaa5..f6b3e136a 100644
--- a/DifferentiationInterfaceTest/CHANGELOG.md
+++ b/DifferentiationInterfaceTest/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased](https://github.com/JuliaDiff/DifferentiationInterface.jl/compare/DifferentiationInterfaceTest-v0.11.0...main)
 
+### Changed
+
+- Test `value_gradient_and_hvp(!)` instead of the deprecated `gradient_and_hvp(!)`, which requires DifferentiationInterface v0.7.22 ([#1086](https://github.com/JuliaDiff/DifferentiationInterface.jl/pull/1086))
+
 ## [0.11.0](https://github.com/JuliaDiff/DifferentiationInterface.jl/compare/DifferentiationInterfaceTest-v0.10.4...DifferentiationInterfaceTest-v0.11.0)
 
 ### Changed
diff --git a/DifferentiationInterfaceTest/Project.toml b/DifferentiationInterfaceTest/Project.toml
index 5f4afe1b6..63f87b32c 100644
--- a/DifferentiationInterfaceTest/Project.toml
+++ b/DifferentiationInterfaceTest/Project.toml
@@ -39,7 +39,7 @@ AllocCheck = "0.2"
 Chairmarks = "1.2.1"
 ComponentArrays = "0.15"
 DataAPI = "1.16.0"
-DifferentiationInterface = "0.7.7"
+DifferentiationInterface = "0.7.22"
 DocStringExtensions = "0.8,0.9"
 ForwardDiff = "0.10.36,1"
 JET = "0.9,0.10,0.11,0.12"
diff --git a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/DifferentiationInterfaceTestChairmarksExt.jl b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/DifferentiationInterfaceTestChairmarksExt.jl
index 3be1a5357..010536ea2 100644
--- a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/DifferentiationInterfaceTestChairmarksExt.jl
+++ b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/DifferentiationInterfaceTestChairmarksExt.jl
@@ -47,8 +47,8 @@ using DifferentiationInterface:
     prepare!_hvp,
     hvp,
     hvp!,
-    gradient_and_hvp,
-    gradient_and_hvp!,
+    value_gradient_and_hvp,
+    value_gradient_and_hvp!,
     prepare_hessian,
     prepare!_hessian,
     hessian,
diff --git a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/benchmark_eval.jl b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/benchmark_eval.jl
index d679f58da..920cf30c5 100644
--- a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/benchmark_eval.jl
+++ b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestChairmarksExt/benchmark_eval.jl
@@ -5,7 +5,7 @@ for op in ALL_OPS
     elseif op == :hessian
         "value_gradient_and_"
     elseif op == :hvp
-        "gradient_and_"
+        "value_gradient_and_"
     else
         "value_and_"
     end
diff --git a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/DifferentiationInterfaceTestJETExt.jl b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/DifferentiationInterfaceTestJETExt.jl
index 40e06046a..a156464c9 100644
--- a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/DifferentiationInterfaceTestJETExt.jl
+++ b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/DifferentiationInterfaceTestJETExt.jl
@@ -45,8 +45,8 @@ using DifferentiationInterface:
     prepare!_hvp,
     hvp,
     hvp!,
-    gradient_and_hvp,
-    gradient_and_hvp!,
+    value_gradient_and_hvp,
+    value_gradient_and_hvp!,
     prepare_hessian,
     prepare!_hessian,
     hessian,
diff --git a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/type_stability_eval.jl b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/type_stability_eval.jl
index 949ea1855..9a7baf920 100644
--- a/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/type_stability_eval.jl
+++ b/DifferentiationInterfaceTest/ext/DifferentiationInterfaceTestJETExt/type_stability_eval.jl
@@ -5,7 +5,7 @@ for op in ALL_OPS
     elseif op == :hessian
         "value_gradient_and_"
     elseif op == :hvp
-        "gradient_and_"
+        "value_gradient_and_"
     else
         "value_and_"
     end
diff --git a/DifferentiationInterfaceTest/src/DifferentiationInterfaceTest.jl b/DifferentiationInterfaceTest/src/DifferentiationInterfaceTest.jl
index c2fa68493..d623e97f4 100644
--- a/DifferentiationInterfaceTest/src/DifferentiationInterfaceTest.jl
+++ b/DifferentiationInterfaceTest/src/DifferentiationInterfaceTest.jl
@@ -62,8 +62,8 @@ using DifferentiationInterface:
     prepare!_hvp,
     hvp,
     hvp!,
-    gradient_and_hvp,
-    gradient_and_hvp!,
+    value_gradient_and_hvp,
+    value_gradient_and_hvp!,
     prepare_hessian,
     prepare!_hessian,
     hessian,
diff --git a/DifferentiationInterfaceTest/src/tests/allocs_eval.jl b/DifferentiationInterfaceTest/src/tests/allocs_eval.jl
index 2061d1872..ec8ab23fe 100644
--- a/DifferentiationInterfaceTest/src/tests/allocs_eval.jl
+++ b/DifferentiationInterfaceTest/src/tests/allocs_eval.jl
@@ -10,7 +10,7 @@ for op in ALL_OPS
     elseif op == :hessian
         "value_gradient_and_"
     elseif op == :hvp
-        "gradient_and_"
+        "value_gradient_and_"
     else
         "value_and_"
     end
diff --git a/DifferentiationInterfaceTest/src/tests/correctness_eval.jl b/DifferentiationInterfaceTest/src/tests/correctness_eval.jl
index ef76414b9..5142a7228 100644
--- a/DifferentiationInterfaceTest/src/tests/correctness_eval.jl
+++ b/DifferentiationInterfaceTest/src/tests/correctness_eval.jl
@@ -12,7 +12,7 @@ for op in ALL_OPS
     elseif op == :hessian
         "value_gradient_and_"
     elseif op == :hvp
-        "gradient_and_"
+        "value_gradient_and_"
     else
         "value_and_"
     end
@@ -766,12 +766,14 @@ for op in ALL_OPS
                 ((), (prep,), (prep_nostrict,), (prep_same,))
             end
             foreach(preptup_cands_val) do preptup_val
-                res1_out1_val, res2_out1_val = $val_and_op(
+                y_out1_val, res1_out1_val, res2_out1_val = $val_and_op(
                     f, preptup_val..., ba, x, t, contexts...
                 )
-                res1_out2_val, res2_out2_val = $val_and_op(
+                y_out2_val, res1_out2_val, res2_out2_val = $val_and_op(
                     f, preptup_val..., ba, x, t, contexts...
                 )
+                @test y_out1_val ≈ scen.y
+                @test y_out2_val ≈ scen.y
                 @test res1_out1_val ≈ scen.res1
                 @test res1_out2_val ≈ scen.res1
                 for b in eachindex(scen.res2)
@@ -826,12 +828,14 @@ for op in ALL_OPS
             foreach(preptup_cands_val) do preptup_val
                 res1_in1_val, res2_in1_val = mysimilar(res1), mysimilar(res2)
                 res1_in2_val, res2_in2_val = mysimilar(res1), mysimilar(res2)
-                res1_out1_val, res2_out1_val = $val_and_op!(
+                y_out1_val, res1_out1_val, res2_out1_val = $val_and_op!(
                     f, res1_in1_val, res2_in1_val, preptup_val..., ba, x, t, contexts...
                 )
-                res1_out2_val, res2_out2_val = $val_and_op!(
+                y_out2_val, res1_out2_val, res2_out2_val = $val_and_op!(
                     f, res1_in2_val, res2_in2_val, preptup_val..., ba, x, t, contexts...
                 )
+                @test y_out1_val ≈ scen.y
+                @test y_out2_val ≈ scen.y
                 @test res1_in1_val === res1_out1_val
                 @test res1_in2_val === res1_out2_val
                 @test res1_out1_val ≈ scen.res1
diff --git a/DifferentiationInterfaceTest/src/tests/prep_eval.jl b/DifferentiationInterfaceTest/src/tests/prep_eval.jl
index 583bccd90..3a477835f 100644
--- a/DifferentiationInterfaceTest/src/tests/prep_eval.jl
+++ b/DifferentiationInterfaceTest/src/tests/prep_eval.jl
@@ -7,7 +7,7 @@ for op in ALL_OPS
     elseif op == :hessian
         "value_gradient_and_"
     elseif op == :hvp
-        "gradient_and_"
+        "value_gradient_and_"
     else
         "value_and_"
     end