We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capture some programming patterns used in untyped languages. Although occurrence typing was tied from its inception to set-theoretic types—union types, in particular—it never fully exploited the capabilities of these types. Here we show how, by using set-theoretic types, it is possible to develop a general typing framework that encompasses and generalizes several aspects of current occurrence typing proposals and that can be applied to tackle other problems such as the reconstruction of intersection types for unannotated or partially annotated functions and the optimization of the compilation of gradually typed languages.