For the past 20 years, configuration spaces of graphs have been studied intensively in algebraic topology, geometric group theory, topological robotics, and algebraic geometry. Nevertheless, there are many questions unanswered and much work to be done. This talk will survey the fundamental results and open questions in this area, assuming no prior familiarity. Depending on time, we may touch on some past, present, and future joint work with An, Drummond-Cole, González, Ramos, and Wawrykow.