Seiberg-Witten invariants are useful for distinguishing different smooth structures on the same topological 4-manifold. To compute these invariants one has developed various "gluing formulae" which relate the invariants of different 4-manifolds. As an example I will discuss here a generalized blow-up formula. This formula has been known to experts for a while and has been used previously by several authors, but no complete proof has yet appeared. In this talk and an accompanying seminar talk I will explain how the formula can be derived from a general gluing theorem for monopoles which I established in a recent preprint.