I plan to use this talk to provide a userA's guide for a method described in a book "Large deviation for stochastic processes" by Feng and Kurtz (2006). This is a Hamilton-Jacobi approach to the theory of large deviation for Markov processes. At the heart of it are variational principles just as in classical mechanics. I will start with some basic observations that lead to such formulation. Then I describe the whole scheme and mathematical challenges associated with applications of the theory to concrete examples. Time permitting, I plan to mention one example in statistical mechanics as well as one example in continuum mechanics.