  The 21st century has seen an enormous growth in the development and use of
approximate Bayesian methods. Such methods produce computational solutions to
certain intractable statistical problems that challenge exact methods like
Markov chain Monte Carlo: for instance, models with unavailable likelihoods,
high-dimensional models, and models featuring large data sets. These
approximate methods are the subject of this review. The aim is to help new
researchers in particular -- and more generally those interested in adopting a
Bayesian approach to empirical work -- distinguish between different
approximate techniques; understand the sense in which they are approximate;
appreciate when and why particular methods are useful; and see the ways in
which they can can be combined.
