With the recent resurgence of interest in graph data man- agement, there has been a flurry of research on the design and engineering of graph query languages. On the design side, there is a large body of theoretical results that have been obtained regarding graph languages. On the engineer- ing side, many sophisticated scalable solutions for graph query processing have been developed and put into practice. While both areas are focusing on the study of graph query languages, there has been relatively little work bridging the results on both sides. This tutorial will survey the state of the art in this landscape with a particular focus on uncovering and highlighting indicative research issues that are ripe for collaboration and cross-fertilization between the engineering and theoretical studies of graph database systems.