diff --git a/docs/src/semilinear/Linear.md b/docs/src/semilinear/Linear.md
index fe14d1ffda..b9fbd87954 100644
--- a/docs/src/semilinear/Linear.md
+++ b/docs/src/semilinear/Linear.md
@@ -9,23 +9,40 @@ first_steps("OrdinaryDiffEqLinear", "LieRK4")
 
 ## Full list of solvers
 
+### Time and State-Independent Solvers
+
+```@docs
+LinearExponential
+```
+
+### Time-Dependent and State-Independent Solvers
+
 ```@docs
 MagnusMidpoint
 MagnusLeapfrog
-LieEuler
 MagnusGauss4
 MagnusNC6
 MagnusGL6
 MagnusGL8
 MagnusNC8
 MagnusGL4
+```
+
+### State-Dependent Solvers
+
+```@docs
+LieEuler
 RKMK2
 RKMK4
 LieRK4
 CG2
-CG3
 CG4a
 MagnusAdapt4
 CayleyEuler
-LinearExponential
 ```
+
+### Time and State-Dependent Operators
+
+```@docs
+CG3
+```
\ No newline at end of file
diff --git a/lib/OrdinaryDiffEqLinear/src/algorithms.jl b/lib/OrdinaryDiffEqLinear/src/algorithms.jl
index 3cdbc22fea..1f213c97ee 100644
--- a/lib/OrdinaryDiffEqLinear/src/algorithms.jl
+++ b/lib/OrdinaryDiffEqLinear/src/algorithms.jl
@@ -1,27 +1,26 @@
 # Linear Methods
 
-for Alg in [
-    :MagnusMidpoint,
-    :MagnusLeapfrog,
-    :LieEuler,
-    :MagnusGauss4,
-    :MagnusNC6,
-    :MagnusGL6,
-    :MagnusGL8,
-    :MagnusNC8,
-    :MagnusGL4,
-    :RKMK2,
-    :RKMK4,
-    :LieRK4,
-    :CG2,
-    :CG3,
-    :CG4a
-]
+for (Alg, Description, Ref) in [
+    (:MagnusMidpoint, "Second order Magnus Midpoint method.", "ref TBD"),
+    (:MagnusLeapfrog, "Second order Magnus Leapfrog method.", "ref TBD"),
+    (:LieEuler, "description", "ref TBD"),
+    (:MagnusGauss4, "Fourth order Magnus method approximated using a two stage Gauss quadrature.", "ref TBD"),
+    (:MagnusNC6, "Sixth order Magnus method approximated using Newton-Cotes quadrature.", "ref TBD"),
+    (:MagnusGL6, "Sixth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
+    (:MagnusGL8, "Eighth order Magnus method approximated using Newton-Cotes quadrature.", "ref TBD"),
+    (:MagnusNC8, "Eighth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
+    (:MagnusGL4, "Fourth order Magnus method approximated using Gauss-Legendre quadrature.", "ref TBD"),
+    (:RKMK2, "Second order Runge–Kutta–Munthe-Kaas method.", "ref TBD"),
+    (:RKMK4, "Fourth order Runge–Kutta–Munthe-Kaas method.", "ref TBD"),
+    (:LieRK4, "Fourth order Lie Runge-Kutta method.", "ref TBD"),
+    (:CG2, "Second order Crouch–Grossman method.", "ref TBD"),
+    (:CG3, "Third order Crouch-Grossman method.", "ref TBD"),
+    (:CG4a, " Fourth order Crouch-Grossman method.", "ref TBD")]
     @eval begin
-        @doc generic_solver_docstring("description TBD",
+        @doc generic_solver_docstring($Description,
             $(string(Alg)),
             "Semilinear ODE solver",
-            "ref TBD",
+            $Ref,
             """
             - `krylov`: TBD
             - `m`: TBD
@@ -31,7 +30,7 @@ for Alg in [
             krylov = false,
             m = 30,
             iop = 0,
-        """)
+            """)
         struct $Alg <: OrdinaryDiffEqLinearExponentialAlgorithm
         krylov::Bool
         m::Int
@@ -41,26 +40,31 @@ for Alg in [
     @eval $Alg(; krylov = false, m = 30, iop = 0) = $Alg(krylov, m, iop)
 end
 
-@doc generic_solver_docstring("description TBD",
+@doc generic_solver_docstring("Fourth Order Adaptive Magnus method.",
     "MagnusAdapt4",
     "Semilinear ODE solver",
     "ref TBD", "", "")
 struct MagnusAdapt4 <: OrdinaryDiffEqAdaptiveAlgorithm end
 
-@doc generic_solver_docstring("description TBD",
+@doc generic_solver_docstring("First order method using Cayley transformations.",
     "CayleyEuler",
     "Semilinear ODE solver",
     "ref TBD", "", "")
 struct CayleyEuler <: OrdinaryDiffEqAlgorithm end
 
-@doc generic_solver_docstring("description TBD",
+@doc generic_solver_docstring("Exact solution formula for linear, time-independent problems.",
     "LinearExponential",
     "Semilinear ODE solver",
     "ref TBD",
     """
-    - `krylov`: TBD
-    - `m`: TBD
-    - `iop`: TBD
+    - `krylov`:
+        - `:off`: cache the operator beforehand. Requires Matrix(A) method defined for the operator A.
+        - `:simple`: uses simple Krylov approximations with fixed subspace size m.
+        - `:adaptive`: uses adaptive Krylov approximations with internal timestepping.
+    - `m`: Controls the size of Krylov subspace if `krylov=:simple`, and the initial subspace size if `krylov=:adaptive`.
+    - `iop`: If not zero, determines the length of the incomplete orthogonalization procedure
+            Note that if the linear operator/Jacobian is hermitian,
+            then the Lanczos algorithm will always be used and the IOP setting is ignored.
     """,
     """
     krylov = :off,