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Graph summarization is a well-established problem in large-scale graph data management. Its goal is to produce a summary graph, which is a coarse-grained version of a graph, whose use in substitution for the original graph enables downstream task execution and query processing at scale. Despite the extensive literature on graph summarization, still nowadays query processing on summary graphs is accomplished by either reconstructing the original graph, or in a query-specific manner. No general methods exist that operate on the summary graph only, with no graph reconstruction. In this paper, we fill this gap, and study for the first time general-purpose (approximate) query processing on summary graphs. This is a new important tool to support data-management tasks that rely on scalable graph query processing, including social network analysis. We set the stage of this problem, by devising basic, yet principled algorithms, and thoroughly analyzing their peculiarities and capabilities of performing well in practice, both conceptually and experimentally. The ultimate goal of this work is to make researchers and practitioners aware of this so-far overlooked problem, and define an authoritative starting point to stimulate and drive further research.