In Measures of maximal entropy for surface diffeomorphisms appeared in the Annals, Buzzi, Crovisier and Sarig proved that (from the Abstract) "$C^\infty$-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case".
It is a huge result in smooth dynamics, and it looks like a major result in general to me, although I'm biased towards dynamical systems.