The property of presuppositions to be sometimes preserved through embeddings, albeit often in a weakened form, is called projection. The projection problem consists in formulating the conditions under which the presuppositions of an embedded clause (a) are kept as presuppositions of the superordinate structure, or (b) remain as an invited inference that can be overruled by context, or (c) are canceled. Over the past 25 years it has been recognized that the projection problem is to be solved in the context of a wider theory of presupposition and discourse incrementation.