 The structure of this entry is as follows: Section 1 discusses the basic notion of “preferences over prospects”, which lies at the heart of decision theory. Section 2 describes the development of normative decision theory in terms of ever more powerful and flexible measures of preferences. Section 3 discusses the two best-known versions of EU theory. Section 4 considers the broader significance of EU theory for practical action, inference, and valuing. Section 5 turns to prominent challenges to EU theory, while Section 6 addresses sequential decisions, and how this richer setting bears on debates about rational preferences.