Topological maps have been used in the mobile robot community, starting with Ben Kuipers insightful work on distinctive places and edges that connected them. This map was a variation of the Voronoi diagram, which I use in my work to robot exploration. In this talk, I will put forward a definition of a topological map and show why the Voronoi diagram is a good topological map. Sadly, this is the only example of a good topological map that I can find, and I will talk about some attempts to make good topological maps in higher dimensional spaces. Finally, I will discuss some problems that exploit a topological map to achieve tasks including SLAM, optimal planning, and hybrid controls.