Abstract: Branched expanding maps $f: S^2 \to S^2$ generalize piecewise expanding multimodal maps of the interval and are the object of much recent study (Cannon-Floyd-Parry; Haissinsky-P.; Bonk-Meyer; Meyer; Nekrashevych). Typically, these are presented only indirectly, and one does not have any good "normal forms" for topological conjugacy classes, e.g. smooth, piecewise affine, etc. models. Are these subsumed in the theory of smooth dynamics? This ignorance contrasts greatly with what we know about expanding maps of circles, intervals, and (infra nil) manifolds. I will focus on several different ways of constructing examples: matings (with movies), subdivision rules (with pictures), contracting virtual endomorphisms of orbifold fundamental groups (with algebra formulas) and other rare examples (with exact formulas).