Large graphs are now commonplace, amplifying the fundamental challenges of exploring, navigating, and understanding massive data. Our work tackles critical aspects of graph sensemaking, to create human-in-the-loop network exploration tools. This dissertation is comprised of three research thrusts, in which we combine techniques from data mining, visual analytics, and graph databases to create scalable, adaptive, interaction-driven graph sensemaking tools. (1) Adaptive Local Graph Exploration: our FACETS system introduces an adaptive exploration paradigm for large graphs to guide user towards interesting and surprising content, based on a novel measurement of surprise and subjective user interest using feature-entropy and the Jensen-Shannon divergence. (2) Interactive Graph Querying: VISAGE empowers analysts to create and refine queries in a visual, interactive environment, without having to write in a graph querying language, outperforming conventional query writing and refinement. Our MAGE algorithm locates high quality approximate subgraph matches and scales to large graphs. (3) Summarizing Subgraph Discovery: we introduce VIGOR, a novel system for summarizing graph querying results, providing practical tools and addressing research challenges in interpreting, grouping, comparing, and exploring querying results. This dissertation contributes to visual analytics, data mining, and their intersection through: interactive systems and scalable algorithms; new measures for ranking content; and exploration paradigms that overcome fundamental challenges in visual analytics. Our contributions work synergistically by utilizing the strengths of visual analytics and graph data mining together to forward graph analytics. Advisors/Committee Members: Chau, Duen Horng (Polo) (advisor), Navathe, Shamkant (committee member), Abello, James (committee member), Vreeken, Jilles (committee member), Tong, Hanghang (committee member), Dilkina, Bistra (committee member), Endert, Alex (committee member).