The phenomena of ambiguity and ambiguity aversion, introduced in Daniel Ellsberg's seminal 1961 article, are ubiquitous in the real world and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals' uncertain beliefs can be represented by subjective probabilities (sometimes called personal probabilities or priors). This chapter begins with a review of early notions of subjective probability and Leonard Savage's joint axiomatic formalization of expected utility and subjective probability. It goes on to describe Ellsberg's classic urn paradoxes and the extensive experimental literature they have inspired. It continues with analytical descriptions of the numerous (primarily axiomatic) models of ambiguity aversion which have been developed by economic theorists, and concludes with a discussion of some current theoretical topics and newer examples of ambiguity aversion.