In gauge theories or string vacua with extended supersymmetry, the spectrum of bound states is often discontinuous across certain walls in the space of parameters or moduli. The jump in the total number of states with given conserved charges is captured by certain `wall-crossing formulae' which have been of much interest recently. As I will explain, these formulae follow in an elementary way from a simple physical picture, namely the appearance or loss of multi-centered monopole or black hole solutions. If time permits, I will also explain how these formulae ensure the continuity of multi-instanton corrections to certain couplings in the low energy effective action.