  Motivated in part by understanding average case analysis of fundamental
algorithms in computer science, and in part by the wide array of network data
available over the last decade, a variety of random graph models, with
corresponding processes on these objects, have been proposed over the last few
years. The main goal of this paper is to give an overview of local weak
convergence, which has emerged as a major technique for understanding large
network asymptotics for a wide array of functionals and models. As opposed to a
survey, the main goal is to try to explain some of the major concepts and their
use to junior researchers in the field and indicate potential resources for
further reading.
