This work began as a research paper intended to show how the convergence of nonlinear semigroups associated with a sequence of Markov processes implied the large deviation principle for the sequence. We expected the result to be of little utility for specific applications, since classical convergence results for nonlinear semigroups involve hypotheses that are very difficult to verify, at least using classical methods. We should have recognized at the beginning that the modern theory of viscosity solutions provides the tools needed to overcome the classical difficulties. Once we did recognized that convergence of the nonlinear semigroups could be verified, the method evolved into a unified treatment of large deviation results for Markov processes, and the research “paper” steadily grew into the current volume.