diff --git a/ext/LinearSolveMooncakeExt.jl b/ext/LinearSolveMooncakeExt.jl
index b3179cbcf..161c422aa 100644
--- a/ext/LinearSolveMooncakeExt.jl
+++ b/ext/LinearSolveMooncakeExt.jl
@@ -1,18 +1,19 @@
 module LinearSolveMooncakeExt
 
 using Mooncake
-using Mooncake: @from_chainrules, MinimalCtx, ReverseMode, NoRData, increment!!
+using Mooncake: @from_chainrules, MinimalCtx, ReverseMode, NoRData, increment!!, @is_primitive, primal, zero_fcodual, CoDual, rdata, fdata
 using LinearSolve: LinearSolve, SciMLLinearSolveAlgorithm, init, solve!, LinearProblem,
-                   LinearCache, AbstractKrylovSubspaceMethod, DefaultLinearSolver,
-                   defaultalg_adjoint_eval, solve
+    LinearCache, AbstractKrylovSubspaceMethod, DefaultLinearSolver, LinearSolveAdjoint,
+    defaultalg_adjoint_eval, solve, LUFactorization
 using LinearSolve.LinearAlgebra
+using LazyArrays: @~, BroadcastArray
 using SciMLBase
 
-@from_chainrules MinimalCtx Tuple{typeof(SciMLBase.solve), LinearProblem, Nothing} true ReverseMode
+@from_chainrules MinimalCtx Tuple{typeof(SciMLBase.solve),LinearProblem,Nothing} true ReverseMode
 @from_chainrules MinimalCtx Tuple{
-    typeof(SciMLBase.solve), LinearProblem, SciMLLinearSolveAlgorithm} true ReverseMode
+    typeof(SciMLBase.solve),LinearProblem,SciMLLinearSolveAlgorithm} true ReverseMode
 @from_chainrules MinimalCtx Tuple{
-    Type{<:LinearProblem}, AbstractMatrix, AbstractVector, SciMLBase.NullParameters} true ReverseMode
+    Type{<:LinearProblem},AbstractMatrix,AbstractVector,SciMLBase.NullParameters} true ReverseMode
 
 function Mooncake.increment_and_get_rdata!(f, r::NoRData, t::LinearProblem)
     f.data.A .+= t.A
@@ -29,4 +30,104 @@ function Mooncake.to_cr_tangent(x::Mooncake.PossiblyUninitTangent{T}) where {T}
     end
 end
 
+function Mooncake.increment_and_get_rdata!(f, r::NoRData, t::LinearCache)
+    f.fields.A .+= t.A
+    f.fields.b .+= t.b
+    f.fields.u .+= t.u
+
+    return NoRData()
+end
+
+# rrules for LinearCache
+@from_chainrules MinimalCtx Tuple{typeof(init),LinearProblem,SciMLLinearSolveAlgorithm} true ReverseMode
+@from_chainrules MinimalCtx Tuple{typeof(init),LinearProblem,Nothing} true ReverseMode
+
+# rrules for solve!
+# NOTE - Avoid Mooncake.prepare_gradient_cache, only use Mooncake.prepare_pullback_cache (and therefore Mooncake.value_and_pullback!!)
+# calling Mooncake.prepare_gradient_cache for functions with solve! will activate unsupported Adjoint case exception for below rrules
+# This because in Mooncake.prepare_gradient_cache we reset stacks + state by passing in zero gradient in the reverse pass once.
+# However, if one has a valid cache then they can directly use Mooncake.value_and_gradient!!.
+
+@is_primitive MinimalCtx Tuple{typeof(SciMLBase.solve!),LinearCache,SciMLLinearSolveAlgorithm,Vararg}
+@is_primitive MinimalCtx Tuple{typeof(SciMLBase.solve!),LinearCache,Nothing,Vararg}
+
+function Mooncake.rrule!!(sig::CoDual{typeof(SciMLBase.solve!)}, _cache::CoDual{<:LinearSolve.LinearCache}, _alg::CoDual{Nothing}, args::Vararg{Any,N}; kwargs...) where {N}
+    cache = primal(_cache)
+    assump = OperatorAssumptions()
+    _alg.x = defaultalg(cache.A, cache.b, assump)
+    Mooncake.rrule!!(sig, _cache, _alg, args...; kwargs...)
+end
+
+function Mooncake.rrule!!(::CoDual{typeof(SciMLBase.solve!)}, _cache::CoDual{<:LinearSolve.LinearCache}, _alg::CoDual{<:SciMLLinearSolveAlgorithm}, args::Vararg{Any,N}; alias_A=zero_fcodual(LinearSolve.default_alias_A(
+        _alg.x, _cache.x.A, _cache.x.b)), kwargs...) where {N}
+
+    cache = primal(_cache)
+    alg = primal(_alg)
+    _args = map(primal, args)
+
+    (; A, b, sensealg) = cache
+    A_orig = copy(A)
+    b_orig = copy(b)
+
+    @assert sensealg isa LinearSolveAdjoint "Currently only `LinearSolveAdjoint` is supported for adjoint sensitivity analysis."
+
+    # logic behind caching `A` and `b` for the reverse pass based on rrule above for SciMLBase.solve
+    if sensealg.linsolve === missing
+        if !(alg isa LinearSolve.AbstractFactorization || alg isa LinearSolve.AbstractKrylovSubspaceMethod ||
+             alg isa LinearSolve.DefaultLinearSolver)
+            A_ = alias_A ? deepcopy(A) : A
+        end
+    else
+        A_ = deepcopy(A)
+    end
+
+    sol = zero_fcodual(solve!(cache))
+    cache.A = A_orig
+    cache.b = b_orig
+
+    function solve!_adjoint(::NoRData)
+        ∂∅ = NoRData()
+        cachenew = init(LinearProblem(cache.A, cache.b), LUFactorization(), _args...; kwargs...)
+        new_sol = solve!(cachenew)
+        ∂u = sol.dx.data.u
+
+        if sensealg.linsolve === missing
+            λ = if cache.cacheval isa Factorization
+                cache.cacheval' \ ∂u
+            elseif cache.cacheval isa Tuple && cache.cacheval[1] isa Factorization
+                first(cache.cacheval)' \ ∂u
+            elseif alg isa AbstractKrylovSubspaceMethod
+                invprob = LinearProblem(adjoint(cache.A), ∂u)
+                solve(invprob, alg; cache.abstol, cache.reltol, cache.verbose).u
+            elseif alg isa DefaultLinearSolver
+                LinearSolve.defaultalg_adjoint_eval(cache, ∂u)
+            else
+                invprob = LinearProblem(adjoint(A_), ∂u) # We cached `A`
+                solve(invprob, alg; cache.abstol, cache.reltol, cache.verbose).u
+            end
+        else
+            invprob = LinearProblem(adjoint(A_), ∂u) # We cached `A`
+            λ = solve(
+                invprob, sensealg.linsolve; cache.abstol, cache.reltol, cache.verbose).u
+        end
+
+        tu = adjoint(new_sol.u)
+        ∂A = BroadcastArray(@~ .-(λ .* tu))
+        ∂b = λ
+
+        if (iszero(∂b) || iszero(∂A)) && !iszero(tu)
+            error("Adjoint case currently not handled. Instead of using `solve!(cache); s1 = copy(cache.u) ...`, use `sol = solve!(cache); s1 = copy(sol.u)`.")
+        end
+
+        fdata(_cache.dx).fields.A .+= ∂A
+        fdata(_cache.dx).fields.b .+= ∂b
+        fdata(_cache.dx).fields.u .+= ∂u
+
+        # rdata for cache is a struct with NoRdata field values
+        return (∂∅, rdata(_cache.dx), ∂∅, ntuple(_ -> ∂∅, length(args))...)
+    end
+
+    return sol, solve!_adjoint
+end
+
 end
\ No newline at end of file
diff --git a/src/adjoint.jl b/src/adjoint.jl
index 281a1ee69..4ecc5b260 100644
--- a/src/adjoint.jl
+++ b/src/adjoint.jl
@@ -99,3 +99,19 @@ function CRC.rrule(::Type{<:LinearProblem}, A, b, p; kwargs...)
     ∇prob(∂prob) = (NoTangent(), ∂prob.A, ∂prob.b, ∂prob.p)
     return prob, ∇prob
 end
+
+function CRC.rrule(T::typeof(LinearSolve.init), prob::LinearSolve.LinearProblem, alg::Nothing, args...; kwargs...)
+    assump = OperatorAssumptions(issquare(prob.A))
+    alg = defaultalg(prob.A, prob.b, assump)
+    CRC.rrule(T, prob, alg, args...; kwargs...)
+end
+
+function CRC.rrule(::typeof(LinearSolve.init), prob::LinearSolve.LinearProblem, alg::Union{LinearSolve.SciMLLinearSolveAlgorithm,Nothing}, args...; kwargs...)
+    init_res = LinearSolve.init(prob, alg)
+    function init_adjoint(∂init)
+        ∂prob = LinearProblem(∂init.A, ∂init.b, NoTangent())
+        return NoTangent(), ∂prob, NoTangent(), ntuple((_ -> NoTangent(), length(args))...)
+    end
+
+    return init_res, init_adjoint
+end
diff --git a/test/nopre/mooncake.jl b/test/nopre/mooncake.jl
index bbd9c5196..c50a89b45 100644
--- a/test/nopre/mooncake.jl
+++ b/test/nopre/mooncake.jl
@@ -11,9 +11,7 @@ b1 = rand(n);
 
 function f(A, b1; alg = LUFactorization())
     prob = LinearProblem(A, b1)
-
     sol1 = solve(prob, alg)
-
     s1 = sol1.u
     norm(s1)
 end
@@ -153,3 +151,146 @@ for alg in (
     @test results[1] ≈ fA(A)
     @test mooncake_gradient ≈ fd_jac rtol = 1e-5
 end
+
+# Tests for solve! and init rrules.
+n = 4
+A = rand(n, n);
+b1 = rand(n);
+b2 = rand(n);
+
+function f_(A, b1, b2; alg=LUFactorization())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+f_primal = f_(copy(A), copy(b1), copy(b2))
+rule = Mooncake.build_rrule(f_, copy(A), copy(b1), copy(b2))
+value, gradient = Mooncake.value_and_pullback!!(
+    rule, 1.0,
+    f_, copy(A), copy(b1), copy(b2)
+)
+
+dA2 = ForwardDiff.gradient(x -> f_(x, eltype(x).(b1), eltype(x).(b2)), copy(A))
+db12 = ForwardDiff.gradient(x -> f_(eltype(x).(A), x, eltype(x).(b2)), copy(b1))
+db22 = ForwardDiff.gradient(x -> f_(eltype(x).(A), eltype(x).(b1), x), copy(b2))
+
+@test value == f_primal
+@test gradient[2] ≈ dA2
+@test gradient[3] ≈ db12
+@test gradient[4] ≈ db22
+
+function f_2(A, b1, b2; alg=RFLUFactorization())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+f_primal = f_2(copy(A), copy(b1), copy(b2))
+rule = Mooncake.build_rrule(f_2, copy(A), copy(b1), copy(b2))
+value, gradient = Mooncake.value_and_pullback!!(
+    rule, 1.0,
+    f_2, copy(A), copy(b1), copy(b2)
+)
+
+dA2 = ForwardDiff.gradient(x -> f_2(x, eltype(x).(b1), eltype(x).(b2)), copy(A))
+db12 = ForwardDiff.gradient(x -> f_2(eltype(x).(A), x, eltype(x).(b2)), copy(b1))
+db22 = ForwardDiff.gradient(x -> f_2(eltype(x).(A), eltype(x).(b1), x), copy(b2))
+
+@test value == f_primal
+@test gradient[2] ≈ dA2
+@test gradient[3] ≈ db12
+@test gradient[4] ≈ db22
+
+function f_3(A, b1, b2; alg=KrylovJL_GMRES())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    s1 = copy(solve!(cache).u)
+    cache.b = b2
+    s2 = solve!(cache).u
+    norm(s1 + s2)
+end
+
+f_primal = f_3(copy(A), copy(b1), copy(b2))
+rule = Mooncake.build_rrule(f_3, copy(A), copy(b1), copy(b2))
+value, gradient = Mooncake.value_and_pullback!!(
+    rule, 1.0,
+    f_3, copy(A), copy(b1), copy(b2)
+)
+
+dA2 = ForwardDiff.gradient(x -> f_3(x, eltype(x).(b1), eltype(x).(b2)), copy(A))
+db12 = ForwardDiff.gradient(x -> f_3(eltype(x).(A), x, eltype(x).(b2)), copy(b1))
+db22 = ForwardDiff.gradient(x -> f_3(eltype(x).(A), eltype(x).(b1), x), copy(b2))
+
+@test value == f_primal
+@test gradient[2] ≈ dA2
+@test gradient[3] ≈ db12
+@test gradient[4] ≈ db22
+
+function f_4(A, b1, b2; alg=LUFactorization())
+    prob = LinearProblem(A, b1)
+    cache = init(prob, alg)
+    solve!(cache)
+    s1 = copy(cache.u)
+    cache.b = b2
+    solve!(cache)
+    s2 = copy(cache.u)
+    norm(s1 + s2)
+end
+
+A = rand(n, n);
+b1 = rand(n);
+b2 = rand(n);
+f_primal = f_4(copy(A), copy(b1), copy(b2))
+
+rule = Mooncake.build_rrule(f_4, copy(A), copy(b1), copy(b2))
+@test_throws "Adjoint case currently not handled" Mooncake.value_and_pullback!!(
+    rule, 1.0,
+    f_4, copy(A), copy(b1), copy(b2)
+)
+
+# dA2 = ForwardDiff.gradient(x -> f_4(x, eltype(x).(b1), eltype(x).(b2)), copy(A))
+# db12 = ForwardDiff.gradient(x -> f_4(eltype(x).(A), x, eltype(x).(b2)), copy(b1))
+# db22 = ForwardDiff.gradient(x -> f_4(eltype(x).(A), eltype(x).(b1), x), copy(b2))
+
+# @test value == f_primal
+# @test grad[2] ≈ dA2
+# @test grad[3] ≈ db12
+# @test grad[4] ≈ db22
+
+A = rand(n, n);
+b1 = rand(n);
+
+function fnice(A, b, alg)
+    prob = LinearProblem(A, b)
+    sol1 = solve(prob, alg)
+    return sum(sol1.u)
+end
+
+@testset for alg in (
+    LUFactorization(),
+    RFLUFactorization(),
+    KrylovJL_GMRES()
+)
+    # for B
+    fb_closure = b -> fnice(A, b, alg)
+    fd_jac_b = FiniteDiff.finite_difference_jacobian(fb_closure, b1) |> vec
+
+    val, en_jac = Mooncake.value_and_gradient!!(
+        prepare_gradient_cache(fnice, copy(A), copy(b1), alg),
+        fnice, copy(A), copy(b1), alg
+    )
+    @test en_jac[3] ≈ fd_jac_b rtol = 1e-5
+
+    # For A
+    fA_closure = A -> fnice(A, b1, alg)
+    fd_jac_A = FiniteDiff.finite_difference_jacobian(fA_closure, A) |> vec
+    A_grad = en_jac[2] |> vec
+    @test A_grad ≈ fd_jac_A rtol = 1e-5
+end
\ No newline at end of file