Planar polygons; Regular, convex, almost convex, staircase and row convex

In recent years there has been renewed interest in a variety of models of planar polygons. These are combinatorial models of interest in their own right. In addition, they have application to such diverse areas as Computer Science and Polymer Chemistry. They also represent increasingly close approximations to the important unsolved problem of self‐avoiding polygons. We review the known exact solutions, and discuss the known numerical results for the self‐avoiding polygon problem. In addition we discuss the enumeration by area, instead of the more usual expansion parameter of perimeter, and discuss the two‐variable generating function, expanded in terms of both area and perimeter.