Ergodic theory of dispersing billiards was developed in 1970s-1980s. An important part of the theory is the analysis of the structure of the sets where the billiard map is discontinuous. They were assumed to be smooth manifolds till recently, when a new pathological type of behavior of these sets was found. Thus a reconsideration of earlier arguments was needed.
I'll review the recent work which recover the ergodicity results, explain the main difficulties and some further progress.