Simultaneous Graph Drawing

Given a set of planar graphs on the same vertex set one can ask for a simultaneous graph drawing, that is, a placement of the vertices that allows all graphs to be drawn in a planar fashion (the different graphs can intersect each other, but not themselves). The problem becomes nontrivial if one restricts the drawings, for example to straight-line drawings. We will survey some recent results, concentrating on questions of computational complexity.