Abstract: Experimental evidence strongly suggests that subjects facing a decision under uncertainty often find it difficult to assess the relative likelihood of certain events; decision theorists deem such events 'ambiguous'. Furthermore, subjects generally dislike options (acts) whose final outcome depends upon the realization of such ambiguous events; that is, they are 'ambiguity-averse'. This article surveys the main decision-theoretic models developed since the mid-1980s to accommodate ambiguity and ambiguity aversion, including Choquet-expected utility (Schmeidler. Econometrica 57: 571–87, 1989) and maxmin expected utility (Gilboa and Schmeidler. J Math Econ 18: 141–53, 1989). More recent developments in the theory of ambiguity are also briefly summarized.