  Stein's method compares probability distributions through the study of a
class of linear operators called Stein operators. While mainly studied in
probability and used to underpin theoretical statistics, Stein's method has led
to significant advances in computational statistics in recent years. The goal
of this survey is to bring together some of these recent developments and, in
doing so, to stimulate further research into the successful field of Stein's
method and statistics. The topics we discuss include tools to benchmark and
compare sampling methods such as approximate Markov chain Monte Carlo,
deterministic alternatives to sampling methods, control variate techniques,
parameter estimation and goodness-of-fit testing.
