Inspired by the functional Ito calculus introduced by B. Dupire, a new theory of PDEs for possibly non-Markov stochastic processes was developed. Dupire's original motivation was to provide a unified treatment of path-dependent derivatives in finance. Since then, many applications have been developed thanks to the newly introduced notion of viscosity solutions of such equations. We review the existence and uniqueness results, and we provide some applications to stochastic control of non-Markovian systems and Monte Carlo approximation of nonlinear (path-)PDEs.