A method will be described to determine generating functions for certain classes of simple walks on the square lattice, while keeping track of their winding angle around the origin. Together with a reflection principle the method can be used to count certain simple walks in wedges of various opening angles, and this is shown to lead in particular to a new proof of the counting of Gessel excursions. If time permits, I'll discuss a connection with the enumeration of planar maps and O(n) loop models.