A tiling of a surface is a covering of the surface by polygons without gaps or overlaps such as in the icosahedral tiling of the sphere. For highly symmetric tilings the geometry of the tiling  is controlled by structure of the symmetry group of the tiling.  The talk gives a quick overview of the link between the tilings and then lists several problems suitable for undergraduate research. Published results of one student collaboration for the summer 1997 and 1998  program are given, with a link to a published paper combining their results, with those of later students and my own results.