The following is an extended version of a talk given at the Kinosaki
Symposium on Algebraic Geometry in October 2011. The aim is to give an overview
of product-quotient surfaces, the results that have been proven so far in
collaboration with several different authors as well as pointing out some of
the the problems that are still open.Comment: Appeared in the proceedings of the Kinosaki Algebraic Geometry
Symopsium held in October 201
