diff --git a/Project.toml b/Project.toml
index 37126969..7d9feefb 100644
--- a/Project.toml
+++ b/Project.toml
@@ -23,8 +23,8 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 [compat]
 CodecBzip2 = "0.7.2, 0.8"
 CodecZlib = "0.7.0"
-Krylov = "0.8, 0.9"
-LDLFactorizations = "0.8, 0.9, 0.10"
+Krylov = "0.10"
+LDLFactorizations = "0.10"
 LinearOperators = "2.0"
 MathOptInterface = "1"
 QPSReader = "0.2"
diff --git a/src/KKT/Krylov/defs.jl b/src/KKT/Krylov/defs.jl
index d8e37345..61fa1fda 100644
--- a/src/KKT/Krylov/defs.jl
+++ b/src/KKT/Krylov/defs.jl
@@ -1,48 +1,29 @@
 const _KRYLOV_SPD = Union{
-    Krylov.CgSolver,
-    Krylov.CrSolver,
+    Krylov.CgWorkspace,
+    Krylov.CrWorkspace,
+    Krylov.CarWorkspace,
 }
 
 const _KRYLOV_SID = Union{
-    Krylov.MinresSolver,
-    Krylov.MinresQlpSolver,
-    Krylov.SymmlqSolver
+    Krylov.MinresWorkspace,
+    Krylov.MinaresWorkspace,
+    Krylov.MinresQlpWorkspace,
+    Krylov.SymmlqWorkspace
 }
 
 const _KRYLOV_SQD = Union{
-    Krylov.TricgSolver,
-    Krylov.TrimrSolver,
+    Krylov.TricgWorkspace,
+    Krylov.TrimrWorkspace,
 }
 
 const _KRYLOV_LN = Union{
-    Krylov.LnlqSolver,
-    Krylov.CraigSolver,
-    Krylov.CraigmrSolver,
+    Krylov.LnlqWorkspace,
+    Krylov.CraigWorkspace,
+    Krylov.CraigmrWorkspace,
 }
 
 const _KRYLOV_LS = Union{
-    Krylov.LslqSolver,
-    Krylov.LsqrSolver,
-    Krylov.LsmrSolver,
+    Krylov.LslqWorkspace,
+    Krylov.LsqrWorkspace,
+    Krylov.LsmrWorkspace,
 }
-
-# Helper functions
-for (KS, fun) in [
-    (Krylov.CgSolver,Krylov.cg!)
-    (Krylov.CrSolver,Krylov.cr!)
-    (Krylov.MinresSolver,Krylov.minres!)
-    (Krylov.MinresQlpSolver,Krylov.minres_qlp!)
-    (Krylov.SymmlqSolver,Krylov.symmlq!)
-    (Krylov.TricgSolver,Krylov.tricg!)
-    (Krylov.TrimrSolver,Krylov.trimr!)
-    (Krylov.LnlqSolver,Krylov.lnlq!)
-    (Krylov.CraigSolver,Krylov.craig!)
-    (Krylov.CraigmrSolver,Krylov.craigmr!)
-    (Krylov.LslqSolver,Krylov.lslq!)
-    (Krylov.LsqrSolver,Krylov.lsqr!)
-    (Krylov.LsmrSolver,Krylov.lsmr!)
-]
-    @eval begin
-        @inline _krylov!(solver::$KS, args...; kwargs...) = $(fun)(solver, args...; kwargs...)
-    end
-end
diff --git a/src/KKT/Krylov/krylov.jl b/src/KKT/Krylov/krylov.jl
index 7353bb31..5480a061 100644
--- a/src/KKT/Krylov/krylov.jl
+++ b/src/KKT/Krylov/krylov.jl
@@ -14,12 +14,12 @@ import ..KKT: setup, update!, solve!
 include("defs.jl")
 
 """
-    Backend{KS<:Krylov.KrylovSolver,V<:AbstractVector}
+    Backend{KS<:Krylov.KrylovWorkspace,V<:AbstractVector}
 
 [Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl)-based backend for solving linear systems.
 
 The type is parametrized by:
-* `KS<:Krylov.KrylovSolver`: workspace type for the Krylov method.
+* `KS<:Krylov.KrylovWorkspace`: workspace type for the Krylov method.
     Also defines the Krylov method to be used.
 * `V<:AbstractVector`: the vector storage type used within the Krylov method.
     This should be set to `Vector{T}` (for arithmetic `T`) unless, e.g., one uses a GPU.
@@ -31,15 +31,15 @@ See the [Krylov.jl documentation](https://juliasmoothoptimizers.github.io/Krylov
 All the following examples assume everything runs on a CPU in `Float64` arithmetic.
 * To use the conjugate gradient:
 ```julia
-backend = KKT.TlpKrylov.Backend(Krylov.CgSolver, Vector{Float64})
+backend = KKT.TlpKrylov.Backend(Krylov.CgWorkspace, Vector{Float64})
 ```
 * To use MINRES:
 ```julia
-backend = KKT.TlpKrylov.Backend(Krylov.MinresSolver, Vector{Float64})
+backend = KKT.TlpKrylov.Backend(Krylov.MinresWorkspace, Vector{Float64})
 ```
 """
-struct Backend{KS,V} <: AbstractKKTBackend
-    krylov_solver::Type{KS}
+struct Backend{KW,V} <: AbstractKKTBackend
+    krylov_workspace::Type{KW}
     vector_storage::Type{V}
 end
 
diff --git a/src/KKT/Krylov/sid.jl b/src/KKT/Krylov/sid.jl
index fae6d49c..e1f35272 100644
--- a/src/KKT/Krylov/sid.jl
+++ b/src/KKT/Krylov/sid.jl
@@ -1,7 +1,7 @@
 """
     SIDSolver
 """
-mutable struct SIDSolver{T,V,Ta,KL,KS} <: AbstractKrylovSolver{T}
+mutable struct SIDSolver{T,V,Ta,KL,KW} <: AbstractKrylovSolver{T}
     # Problem data
     m::Int
     n::Int
@@ -21,15 +21,15 @@ mutable struct SIDSolver{T,V,Ta,KL,KS} <: AbstractKrylovSolver{T}
     # Krylov solver & related options
     atol::T
     rtol::T
-    krylov_solver::KS
+    krylov_workspace::KW
 
     # TODO: preconditioner
 end
 
-backend(kkt::SIDSolver) = "$(typeof(kkt.krylov_solver))"
+backend(kkt::SIDSolver) = "$(typeof(kkt.krylov_workspace))"
 linear_system(kkt::SIDSolver) = "K2"
 
-function setup(A, ::K2, backend::Backend{KS,V}) where{KS<:_KRYLOV_SID,V}
+function setup(A, ::K2, backend::Backend{KW,V}) where{KW<:_KRYLOV_SID,V}
     Ta = typeof(A)
     T = eltype(A)
     T == eltype(V) || error("eltype(A)=$T incompatible with eltype of Krylov vector storage $V.")
@@ -66,15 +66,15 @@ function setup(A, ::K2, backend::Backend{KS,V}) where{KS<:_KRYLOV_SID,V}
     # Allocate Krylov solver's workspace
     atol = sqrt(eps(T))
     rtol = sqrt(eps(T))
-    krylov_solver = KS(m+n, m+n, V)
+    krylov_workspace = KW(m+n, m+n, V)
 
-    return SIDSolver{T,V,Ta,typeof(opK),typeof(krylov_solver)}(
+    return SIDSolver{T,V,Ta,typeof(opK),typeof(krylov_workspace)}(
         m, n, A,
         θ, regP, regD,
         Θp, Θd, ξ,
         opK,
         atol, rtol,
-        krylov_solver
+        krylov_workspace
     )
 end
 
@@ -97,11 +97,11 @@ function solve!(dx, dy, kkt::SIDSolver{T}, ξp, ξd) where{T}
     @views copyto!(kkt.ξ[(m+1):(m+n)], ξd)
 
     # Solve the augmented system
-    _krylov!(kkt.krylov_solver, kkt.opK, kkt.ξ; atol=kkt.atol, rtol=kkt.rtol)
+    krylov_solve!(kkt.krylov_workspace, kkt.opK, kkt.ξ; atol=kkt.atol, rtol=kkt.rtol)
 
     # Recover dx, dy
-    copyto!(dx, kkt.krylov_solver.x[1:n])
-    copyto!(dy, kkt.krylov_solver.x[(n+1):(m+n)])
+    copyto!(dx, kkt.krylov_workspace.x[1:n])
+    copyto!(dy, kkt.krylov_workspace.x[(n+1):(m+n)])
 
     # TODO: iterative refinement (?)
     return nothing
diff --git a/src/KKT/Krylov/spd.jl b/src/KKT/Krylov/spd.jl
index b3d5607d..ec19819c 100644
--- a/src/KKT/Krylov/spd.jl
+++ b/src/KKT/Krylov/spd.jl
@@ -97,7 +97,7 @@ function solve!(dx, dy, kkt::SPDSolver{T}, ξp, ξd) where{T}
     mul!(kkt.ξ, kkt.A, kkt.D * ξd, true, true)
 
     # Solve the normal equations
-    _krylov!(kkt.krylov_solver, kkt.opK, kkt.ξ; atol=kkt.atol, rtol=kkt.rtol)
+    krylov_solve!(kkt.krylov_solver, kkt.opK, kkt.ξ; atol=kkt.atol, rtol=kkt.rtol)
     copyto!(dy, kkt.krylov_solver.x)
 
     # Recover dx
diff --git a/src/KKT/Krylov/sqd.jl b/src/KKT/Krylov/sqd.jl
index f2449d94..c1a6e76d 100644
--- a/src/KKT/Krylov/sqd.jl
+++ b/src/KKT/Krylov/sqd.jl
@@ -84,7 +84,7 @@ function solve!(dx, dy, kkt::SQDSolver{T}, ξp, ξd) where{T}
     copyto!(kkt.ξd, ξd)
 
     # Solve the augmented system
-    _krylov!(kkt.krylov_solver, kkt.A, kkt.ξp, kkt.ξd;
+    krylov_solve!(kkt.krylov_solver, kkt.A, kkt.ξp, kkt.ξd;
         M=kkt.Θd⁻¹,
         N=kkt.Θp⁻¹,
         atol=kkt.atol,
diff --git a/test/KKT/Krylov/sid.jl b/test/KKT/Krylov/sid.jl
index d594f5ff..fd15baba 100644
--- a/test/KKT/Krylov/sid.jl
+++ b/test/KKT/Krylov/sid.jl
@@ -11,7 +11,7 @@ function test_krylov_sid(T, ksolver)
 end
 
 @testset "SID" begin
-    for T in TvTYPES, ksolver in [MinresSolver, MinresQlpSolver, SymmlqSolver]
+    for T in TvTYPES, ksolver in [MinresWorkspace, MinaresWorkspace, MinresQlpWorkspace, SymmlqWorkspace]
         @testset "$ksolver ($T)" begin
             test_krylov_sid(T, ksolver)
         end
diff --git a/test/KKT/Krylov/spd.jl b/test/KKT/Krylov/spd.jl
index ce13b9f9..e6c88c4a 100644
--- a/test/KKT/Krylov/spd.jl
+++ b/test/KKT/Krylov/spd.jl
@@ -11,7 +11,7 @@ function test_krylov_spd(T, ksolver)
 end
 
 @testset "SPD" begin
-    for T in TvTYPES, ksolver in [CgSolver, MinresSolver]
+    for T in TvTYPES, ksolver in [CgWorkspace, CarWorkspace]
         @testset "$ksolver ($T)" begin
             test_krylov_spd(T, ksolver)
         end
diff --git a/test/KKT/Krylov/sqd.jl b/test/KKT/Krylov/sqd.jl
index edfe401f..60abaa62 100644
--- a/test/KKT/Krylov/sqd.jl
+++ b/test/KKT/Krylov/sqd.jl
@@ -11,7 +11,7 @@ function test_krylov_sqd(T, ksolver)
 end
 
 @testset "SQD" begin
-    for T in TvTYPES, ksolver in [TricgSolver, TrimrSolver]
+    for T in TvTYPES, ksolver in [TricgWorkspace, TrimrWorkspace]
         @testset "$ksolver ($T)" begin
             test_krylov_sqd(T, ksolver)
         end
diff --git a/test/Project.toml b/test/Project.toml
index ad12cc25..b9171ab3 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -7,5 +7,5 @@ TOML = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-Krylov = "0.8, 0.9"
+Krylov = "0.10"
 MathOptInterface= "1"