  This document is due to appear as a chapter of the forthcoming Handbook of
Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M.
Beaumont.
  Since the earliest work on ABC, it has been recognised that using summary
statistics is essential to produce useful inference results. This is because
ABC suffers from a curse of dimensionality effect, whereby using high
dimensional inputs causes large approximation errors in the output. It is
therefore crucial to find low dimensional summaries which are informative about
the parameter inference or model choice task at hand. This chapter reviews the
methods which have been proposed to select such summaries, extending the
previous review paper of Blum et al. (2013) with recent developments. Related
theoretical results on the ABC curse of dimensionality and sufficiency are also
discussed.
