Reflecting diffusions arise in many applications: from stochastic networks, to singular stochastic control, to the motion of physical particles, etc.. In many examples the domain in which the reflecting diffusion is to be confined is nonsmooth or the direction of reflection varies nonsmoothly: in these cases it is not obvious that a reflecting diffusion with the prescribed direction of reflection exists and is uniquely characterized. After reviewing the literature, in which the works by Dupuis and Ishii play a central role, I will discuss how a recent ergodic theorem for inhomogeneous killed Markov chains allows to extend the 1993 Dupuis and Ishii results to some new classes of domains and directions of reflection. In particular one can obtain existence and uniqueness of a semimartingale reflecting diffusion in a piecewise smooth domain in dimension 2, possibly with cusps, under optimal conditions on the directions of reflection, and one can uniquely characterize obliquely reflecting Brownian motion in some piecewise smooth cones. The talk is based on joint works with T.G. Kurtz.