  The goal of this expository paper is to describe conditions which guarantee a
central limit theorem for functionals of general state space Markov chains.
This is done with a view towards Markov chain Monte Carlo settings and hence
the focus is on the connections between drift and mixing conditions and their
implications. In particular, we consider three commonly cited central limit
theorems and discuss their relationship to classical results for mixing
processes. Several motivating examples are given which range from toy
one-dimensional settings to complicated settings encountered in Markov chain
Monte Carlo.
