This paper surveys some recent developments in equilibrium analysis based on a differential viewpoint. They deal with the structure of the set of equilibria, with the study of regular and singular economies, with the determinateness of the number of equilibria, and with an application to characterizing economies having a unique equilibrium. Equilibrium analysis from the differential viewpoint turns out to be formally similar to models encountered in Thom's catastrophe theory understood as a general theory of bifurcation phenomena.