Abstract: This paper discusses the presupposition theory in pragmatics and illustrates several aspects of the theory,including semantic presupposition,pragmatic presupposition,focus，mutual knowledge,the relations between presupposition and context,and presupposition triggers.It also discusses the characteristics of presupposition:the defeasibility and projection problem.With further development of the notion of presupposition and its enlarging scope,research on presupposition has moved from the linguistic forms of surface structure to the aspects of situations and social cultural background.

Key words: presupposition；focus, mutual knowledge；presupposition trigger；projection of presupposition；defeasibility