  Afriat's Theorem (1967) states that a dataset can be thought of as being
generated by a consumer maximizing a continuous and increasing utility function
if and only if it is free of revealed preference cycles containing a strict
relation. The latter property is often known by its acronym, GARP (for
generalized axiom of revealed preference). This paper surveys extensions and
applications of Afriat's seminal result. We focus on those results where the
consistency of a dataset with the maximization of a utility function satisfying
some property can be characterized by a suitably modified version of GARP.
