diff --git a/HISTORY.md b/HISTORY.md
index 039ac6bb9..381b264a6 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -1,3 +1,23 @@
+# 0.42.0
+
+## External sampler interface
+
+The interface for defining an external sampler has been reworked.
+In general, implementations of external samplers should now no longer need to depend on Turing.
+This is because the interface functions required have been shifted upstream to AbstractMCMC.jl.
+
+In particular, you now only need to define the following functions:
+
+  - AbstractMCMC.step(rng::Random.AbstractRNG, model::AbstractMCMC.LogDensityModel, ::MySampler; kwargs...) (and also a method with `state`, and the corresponding `step_warmup` methods if needed)
+  - AbstractMCMC.getparams(::MySamplerState)               -> Vector{<:Real}
+  - AbstractMCMC.getstats(::MySamplerState)                -> NamedTuple
+  - AbstractMCMC.requires_unconstrained_space(::MySampler) -> Bool (default `true`)
+
+This means that you only need to depend on AbstractMCMC.jl.
+As long as the above functions are defined correctly, Turing will be able to use your external sampler.
+
+The `Turing.Inference.isgibbscomponent(::MySampler)` interface function still exists, but in this version the default has been changed to `true`, so you should not need to overload this.
+
 # 0.41.1
 
 The `ModeResult` struct returned by `maximum_a_posteriori` and `maximum_likelihood` can now be wrapped in `InitFromParams()`.
diff --git a/Project.toml b/Project.toml
index cb7b1cb72..23a8af183 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Turing"
 uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
-version = "0.41.1"
+version = "0.42.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -49,11 +49,11 @@ TuringOptimExt = ["Optim", "AbstractPPL"]
 
 [compat]
 ADTypes = "1.9"
-AbstractMCMC = "5.5"
+AbstractMCMC = "5.9"
 AbstractPPL = "0.11, 0.12, 0.13"
 Accessors = "0.1"
-AdvancedHMC = "0.3.0, 0.4.0, 0.5.2, 0.6, 0.7, 0.8"
-AdvancedMH = "0.8"
+AdvancedHMC = "0.8.3"
+AdvancedMH = "0.8.9"
 AdvancedPS = "0.7"
 AdvancedVI = "0.4"
 BangBang = "0.4.2"
diff --git a/src/mcmc/Inference.jl b/src/mcmc/Inference.jl
index 7d25ecd7e..695f9c3aa 100644
--- a/src/mcmc/Inference.jl
+++ b/src/mcmc/Inference.jl
@@ -429,10 +429,10 @@ include("hmc.jl")
 include("mh.jl")
 include("is.jl")
 include("particle_mcmc.jl")
-include("gibbs.jl")
 include("sghmc.jl")
 include("emcee.jl")
 include("prior.jl")
+include("gibbs.jl")
 
 ################
 # Typing tools #
diff --git a/src/mcmc/external_sampler.jl b/src/mcmc/external_sampler.jl
index f8673f6ee..94e9e1706 100644
--- a/src/mcmc/external_sampler.jl
+++ b/src/mcmc/external_sampler.jl
@@ -1,5 +1,5 @@
 """
-    ExternalSampler{S<:AbstractSampler,AD<:ADTypes.AbstractADType,Unconstrained}
+    ExternalSampler{Unconstrained,S<:AbstractSampler,AD<:ADTypes.AbstractADType}
 
 Represents a sampler that does not have a custom implementation of `AbstractMCMC.step(rng,
 ::DynamicPPL.Model, spl)`.
@@ -14,45 +14,59 @@ $(TYPEDFIELDS)
 If you implement a new `MySampler <: AbstractSampler` and want it to work with Turing.jl
 models, there are two options:
 
-1. Directly implement the `AbstractMCMC.step` methods for `DynamicPPL.Model`. This is the
-   most powerful option and is what Turing.jl's in-house samplers do. Implementing this
-   means that you can directly call `sample(model, MySampler(), N)`.
+1. Directly implement the `AbstractMCMC.step` methods for `DynamicPPL.Model`. That is to
+   say, implement `AbstractMCMC.step(rng::Random.AbstractRNG, model::DynamicPPL.Model,
+   sampler::MySampler; kwargs...)` and related methods. This is the most powerful option and
+   is what Turing.jl's in-house samplers do. Implementing this means that you can directly
+   call `sample(model, MySampler(), N)`.
 
-2. Implement a generic `AbstractMCMC.step` method for `AbstractMCMC.LogDensityModel`. This
-   struct wraps an object that obeys the LogDensityProblems.jl interface, so your `step`
+2. Implement a generic `AbstractMCMC.step` method for `AbstractMCMC.LogDensityModel` (the
+   same signature as above except that `model::AbstractMCMC.LogDensityModel`). This struct
+   wraps an object that obeys the LogDensityProblems.jl interface, so your `step`
    implementation does not need to know anything about Turing.jl or DynamicPPL.jl. To use
    this with Turing.jl, you will need to wrap your sampler: `sample(model,
    externalsampler(MySampler()), N)`.
 
 This section describes the latter.
 
-`MySampler` must implement the following methods:
+`MySampler` **must** implement the following methods:
 
 - `AbstractMCMC.step` (the main function for taking a step in MCMC sampling; this is
-  documented in AbstractMCMC.jl)
-- `Turing.Inference.getparams(::DynamicPPL.Model, external_transition)`: How to extract the
-  parameters from the transition returned by your sampler (i.e., the first return value of
-  `step`). There is a default implementation for this method, which is to return
-  `external_transition.θ`.
-
-!!! note
-    In a future breaking release of Turing, this is likely to change to
-    `AbstractMCMC.getparams(::DynamicPPL.Model, external_state)`, with no default method.
-    `Turing.Inference.getparams` is technically an internal method, so the aim here is to
-    unify the interface for samplers at a higher level.
+  documented in AbstractMCMC.jl). This function must return a tuple of two elements, a
+  'transition' and a 'state'.
+
+- `AbstractMCMC.getparams(external_state)`: How to extract the parameters from the **state**
+  returned by your sampler (i.e., the **second** return value of `step`). For your sampler
+  to work with Turing.jl, this function should return a Vector of parameter values. Note that
+  this function does not need to perform any linking or unlinking; Turing.jl will take care of
+  this for you. You should return the parameters *exactly* as your sampler sees them.
+
+- `AbstractMCMC.getstats(external_state)`: Extract sampler statistics corresponding to this
+  iteration from the **state** returned by your sampler (i.e., the **second** return value
+  of `step`). For your sampler to work with Turing.jl, this function should return a
+  `NamedTuple`. If there are no statistics to return, return `NamedTuple()`.
+
+  Note that `getstats` should not include log-probabilities as these will be recalculated by
+  Turing automatically for you.
+
+Notice that both of these functions take the **state** as input, not the **transition**. In
+other words, the transition is completely useless for the external sampler interface. This is
+in line with long-term plans for removing transitions from AbstractMCMC.jl and only using
+states.
 
 There are a few more optional functions which you can implement to improve the integration
 with Turing.jl:
 
-- `Turing.Inference.isgibbscomponent(::MySampler)`: If you want your sampler to function as
-  a component in Turing's Gibbs sampler, you should make this evaluate to `true`.
-
-- `Turing.Inference.requires_unconstrained_space(::MySampler)`: If your sampler requires
+- `AbstractMCMC.requires_unconstrained_space(::MySampler)`: If your sampler requires
   unconstrained space, you should return `true`. This tells Turing to perform linking on the
   VarInfo before evaluation, and ensures that the parameter values passed to your sampler
   will always be in unconstrained (Euclidean) space.
+
+- `Turing.Inference.isgibbscomponent(::MySampler)`: If you want to disallow your sampler
+  from a component in Turing's Gibbs sampler, you should make this evaluate to `false`. Note
+  that the default is `true`, so you should only need to implement this in special cases.
 """
-struct ExternalSampler{S<:AbstractSampler,AD<:ADTypes.AbstractADType,Unconstrained} <:
+struct ExternalSampler{Unconstrained,S<:AbstractSampler,AD<:ADTypes.AbstractADType} <:
        AbstractSampler
     "the sampler to wrap"
     sampler::S
@@ -67,35 +81,26 @@ struct ExternalSampler{S<:AbstractSampler,AD<:ADTypes.AbstractADType,Unconstrain
     # Arguments
     - `sampler::AbstractSampler`: The sampler to wrap.
     - `adtype::ADTypes.AbstractADType`: The automatic differentiation (AD) backend to use.
-    - `unconstrained::Val=Val{true}()`: Value type containing a boolean indicating whether the sampler requires unconstrained space.
+    - `unconstrained::Val`: Value type containing a boolean indicating whether the sampler requires unconstrained space.
     """
     function ExternalSampler(
-        sampler::AbstractSampler,
-        adtype::ADTypes.AbstractADType,
-        (::Val{unconstrained})=Val(true),
+        sampler::AbstractSampler, adtype::ADTypes.AbstractADType, ::Val{unconstrained}
     ) where {unconstrained}
         if !(unconstrained isa Bool)
             throw(
                 ArgumentError("Expected Val{true} or Val{false}, got Val{$unconstrained}")
             )
         end
-        return new{typeof(sampler),typeof(adtype),unconstrained}(sampler, adtype)
+        return new{unconstrained,typeof(sampler),typeof(adtype)}(sampler, adtype)
     end
 end
 
 """
-    requires_unconstrained_space(sampler::ExternalSampler)
-
-Return `true` if the sampler requires unconstrained space, and `false` otherwise.
-"""
-function requires_unconstrained_space(
-    ::ExternalSampler{<:Any,<:Any,Unconstrained}
-) where {Unconstrained}
-    return Unconstrained
-end
-
-"""
-    externalsampler(sampler::AbstractSampler; adtype=AutoForwardDiff(), unconstrained=true)
+    externalsampler(
+        sampler::AbstractSampler;
+        adtype=AutoForwardDiff(),
+        unconstrained=AbstractMCMC.requires_unconstrained_space(sampler),
+    )
 
 Wrap a sampler so it can be used as an inference algorithm.
 
@@ -103,11 +108,15 @@ Wrap a sampler so it can be used as an inference algorithm.
 - `sampler::AbstractSampler`: The sampler to wrap.
 
 # Keyword Arguments
-- `adtype::ADTypes.AbstractADType=ADTypes.AutoForwardDiff()`: The automatic differentiation (AD) backend to use.
-- `unconstrained::Bool=true`: Whether the sampler requires unconstrained space.
+- `adtype::ADTypes.AbstractADType=ADTypes.AutoForwardDiff()`: The automatic differentiation
+  (AD) backend to use.
+- `unconstrained::Bool=AbstractMCMC.requires_unconstrained_space(sampler)`: Whether the
+  sampler requires unconstrained space.
 """
 function externalsampler(
-    sampler::AbstractSampler; adtype=Turing.DEFAULT_ADTYPE, unconstrained::Bool=true
+    sampler::AbstractSampler;
+    adtype=Turing.DEFAULT_ADTYPE,
+    unconstrained::Bool=AbstractMCMC.requires_unconstrained_space(sampler),
 )
     return ExternalSampler(sampler, adtype, Val(unconstrained))
 end
@@ -128,30 +137,21 @@ end
 get_varinfo(state::TuringState) = state.varinfo
 get_varinfo(state::AbstractVarInfo) = state
 
-getparams(::DynamicPPL.Model, transition::AdvancedHMC.Transition) = transition.z.θ
-function getparams(model::DynamicPPL.Model, state::AdvancedHMC.HMCState)
-    return getparams(model, state.transition)
-end
-getstats(transition::AdvancedHMC.Transition) = transition.stat
-
-getparams(::DynamicPPL.Model, transition::AdvancedMH.Transition) = transition.params
-
-# TODO: Do we also support `resume`, etc?
 function AbstractMCMC.step(
     rng::Random.AbstractRNG,
     model::DynamicPPL.Model,
-    sampler_wrapper::ExternalSampler;
+    sampler_wrapper::ExternalSampler{unconstrained};
     initial_state=nothing,
     initial_params, # passed through from sample
     kwargs...,
-)
+) where {unconstrained}
     sampler = sampler_wrapper.sampler
 
     # Initialise varinfo with initial params and link the varinfo if needed.
     varinfo = DynamicPPL.VarInfo(model)
     _, varinfo = DynamicPPL.init!!(rng, model, varinfo, initial_params)
 
-    if requires_unconstrained_space(sampler_wrapper)
+    if unconstrained
         varinfo = DynamicPPL.link(varinfo, model)
     end
 
@@ -166,16 +166,17 @@ function AbstractMCMC.step(
     )
 
     # Then just call `AbstractMCMC.step` with the right arguments.
-    if initial_state === nothing
-        transition_inner, state_inner = AbstractMCMC.step(
+    _, state_inner = if initial_state === nothing
+        AbstractMCMC.step(
             rng,
             AbstractMCMC.LogDensityModel(f),
             sampler;
             initial_params=initial_params_vector,
             kwargs...,
         )
+
     else
-        transition_inner, state_inner = AbstractMCMC.step(
+        AbstractMCMC.step(
             rng,
             AbstractMCMC.LogDensityModel(f),
             sampler,
@@ -185,13 +186,12 @@ function AbstractMCMC.step(
         )
     end
 
-    # NOTE: This is Turing.Inference.getparams, not AbstractMCMC.getparams (!!!!!)
-    # The latter uses the state rather than the transition.
-    # TODO(penelopeysm): Make this use AbstractMCMC.getparams instead
-    new_parameters = Turing.Inference.getparams(f.model, transition_inner)
+    new_parameters = AbstractMCMC.getparams(f.model, state_inner)
     new_vi = DynamicPPL.unflatten(f.varinfo, new_parameters)
+    new_stats = AbstractMCMC.getstats(state_inner)
     return (
-        Transition(f.model, new_vi, transition_inner), TuringState(state_inner, new_vi, f)
+        Turing.Inference.Transition(f.model, new_vi, new_stats),
+        TuringState(state_inner, new_vi, f),
     )
 end
 
@@ -206,16 +206,15 @@ function AbstractMCMC.step(
     f = state.ldf
 
     # Then just call `AdvancedMCMC.step` with the right arguments.
-    transition_inner, state_inner = AbstractMCMC.step(
+    _, state_inner = AbstractMCMC.step(
         rng, AbstractMCMC.LogDensityModel(f), sampler, state.state; kwargs...
     )
 
-    # NOTE: This is Turing.Inference.getparams, not AbstractMCMC.getparams (!!!!!)
-    # The latter uses the state rather than the transition.
-    # TODO(penelopeysm): Make this use AbstractMCMC.getparams instead
-    new_parameters = Turing.Inference.getparams(f.model, transition_inner)
+    new_parameters = AbstractMCMC.getparams(f.model, state_inner)
     new_vi = DynamicPPL.unflatten(f.varinfo, new_parameters)
+    new_stats = AbstractMCMC.getstats(state_inner)
     return (
-        Transition(f.model, new_vi, transition_inner), TuringState(state_inner, new_vi, f)
+        Turing.Inference.Transition(f.model, new_vi, new_stats),
+        TuringState(state_inner, new_vi, f),
     )
 end
diff --git a/src/mcmc/gibbs.jl b/src/mcmc/gibbs.jl
index 7d15829a3..1ff50a646 100644
--- a/src/mcmc/gibbs.jl
+++ b/src/mcmc/gibbs.jl
@@ -3,23 +3,19 @@
 
 Return a boolean indicating whether `spl` is a valid component for a Gibbs sampler.
 
-Defaults to `false` if no method has been defined for a particular algorithm type.
+Defaults to `true` if no method has been defined for a particular sampler.
 """
-isgibbscomponent(::AbstractSampler) = false
-
-isgibbscomponent(::ESS) = true
-isgibbscomponent(::HMC) = true
-isgibbscomponent(::HMCDA) = true
-isgibbscomponent(::NUTS) = true
-isgibbscomponent(::MH) = true
-isgibbscomponent(::PG) = true
+isgibbscomponent(::AbstractSampler) = true
 
 isgibbscomponent(spl::RepeatSampler) = isgibbscomponent(spl.sampler)
-
 isgibbscomponent(spl::ExternalSampler) = isgibbscomponent(spl.sampler)
-isgibbscomponent(::AdvancedHMC.AbstractHMCSampler) = true
-isgibbscomponent(::AdvancedMH.MetropolisHastings) = true
-isgibbscomponent(spl) = false
+
+isgibbscomponent(::IS) = false
+isgibbscomponent(::Prior) = false
+isgibbscomponent(::Emcee) = false
+isgibbscomponent(::SGLD) = false
+isgibbscomponent(::SGHMC) = false
+isgibbscomponent(::SMC) = false
 
 function can_be_wrapped(ctx::DynamicPPL.AbstractContext)
     return DynamicPPL.NodeTrait(ctx) isa DynamicPPL.IsLeaf
diff --git a/test/Project.toml b/test/Project.toml
index 2b5b124b5..73361d794 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -40,9 +40,9 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 
 [compat]
 ADTypes = "1"
-AbstractMCMC = "5"
+AbstractMCMC = "5.9"
 AbstractPPL = "0.11, 0.12, 0.13"
-AdvancedMH = "0.6, 0.7, 0.8"
+AdvancedMH = "0.8.9"
 AdvancedPS = "0.7"
 AdvancedVI = "0.4"
 Aqua = "0.8"
diff --git a/test/mcmc/external_sampler.jl b/test/mcmc/external_sampler.jl
index 56c03c87a..36f53462e 100644
--- a/test/mcmc/external_sampler.jl
+++ b/test/mcmc/external_sampler.jl
@@ -20,16 +20,11 @@ using Turing.Inference: AdvancedHMC
     # Turing declares an interface for external samplers (see docstring for
     # ExternalSampler). We should check that implementing this interface
     # and only this interface allows us to use the sampler in Turing.
-    struct MyTransition{V<:AbstractVector}
-        params::V
-    end
-    # Samplers need to implement `Turing.Inference.getparams`.
-    Turing.Inference.getparams(::DynamicPPL.Model, t::MyTransition) = t.params
-    # State doesn't matter (but we need to carry the params through to the next
-    # iteration).
     struct MyState{V<:AbstractVector}
         params::V
     end
+    AbstractMCMC.getparams(s::MyState) = s.params
+    AbstractMCMC.getstats(s::MyState) = (param_length=length(s.params),)
 
     # externalsamplers must accept LogDensityModel inside their step function.
     # By default Turing gives the externalsampler a LDF constructed with
@@ -58,7 +53,7 @@ using Turing.Inference: AdvancedHMC
         lp, grad = LogDensityProblems.logdensity_and_gradient(ldf, initial_params)
         @test lp isa Real
         @test grad isa AbstractVector{<:Real}
-        return MyTransition(initial_params), MyState(initial_params)
+        return nothing, MyState(initial_params)
     end
     function AbstractMCMC.step(
         rng::Random.AbstractRNG,
@@ -75,7 +70,7 @@ using Turing.Inference: AdvancedHMC
         lp, grad = LogDensityProblems.logdensity_and_gradient(ldf, params)
         @test lp isa Real
         @test grad isa AbstractVector{<:Real}
-        return MyTransition(params), MyState(params)
+        return nothing, MyState(params)
     end
 
     @model function test_external_sampler()
@@ -96,6 +91,7 @@ using Turing.Inference: AdvancedHMC
     @test all(chn[:lp] .== expected_logpdf)
     @test all(chn[:logprior] .== expected_logpdf)
     @test all(chn[:loglikelihood] .== 0.0)
+    @test all(chn[:param_length] .== 2)
 end
 
 function initialize_nuts(model::DynamicPPL.Model)