Belief is introduced as the cognitive act or state in which a proposition is taken to be true, and the psychological theory of belief is reviewed under the headings: belief as a propositional attitude, belief as subjective probability, belief as inference, and belief as association. Apart from its importance as a separate area of cognitive theory, the study of belief is of considerable metatheoretic importance for cognitive theory generally, since belief is an essential part of the definition of cognition. It is argued here that cognitive theories must admit, at least in principle, of a distinction between forms of arousal which imply that a proposition is believed and others which do not. Otherwise it is impossible to model the element of rational judgment, which is a feature of belief and hence of cognition also.