We consider a variation of the classical Erd\H{o}s-Szekeres problems on the
existence and number of convex k-gons and k-holes (empty k-gons) in a set
of n points in the plane. Allowing the k-gons to be non-convex, we show
bounds and structural results on maximizing and minimizing their numbers. Most
noteworthy, for any k and sufficiently large n, we give a quadratic lower
bound for the number of k-holes, and show that this number is maximized by
sets in convex position
