  We survey results about Haar null subsets of (not necessarily locally
compact) Polish groups. The aim of this paper is to collect the fundamental
properties of the various possible definitions of Haar null sets, and also to
review the techniques that may enable the reader to prove results in this area.
We also present several recently introduced ideas, including the notion of Haar
meager sets, which are closely analogous to Haar null sets. We prove some
results in a more general setting than that of the papers where they were
originally proved and prove some results for Haar meager sets which were
already known for Haar null sets.
