Networks naturally capture a host of interactions in the real world spanning from friendships to brain activity. But, given a massive graph, like the Facebook social graph, what can be said about its structure? Which are its most important structures? How does it compare to other networks like Twitter? This talk will focus on my work developing scalable algorithms and models that help us to make sense of large graphs via pattern discovery and similarity analysis. I will begin by presenting VoG, an approach that efficiently summarizes large graphs by finding their most interesting and semantically meaningful structures. Starting from a clutter of millions of nodes and edges, such as the Enron who-mails-whom graph, our Minimum Description Length based algorithm, disentangles the complex graph connectivity and spotlights the structures that ‘best’ describe the graph. Then, for similarity analysis at the graph level, I will introduce the problems of graph comparison and graph alignment. I will conclude by showing how to apply my methods to temporal anomaly detection, brain graph clustering, deanonymization of bipartite (e.g., user-group membership) and unipartite graphs, and more.