There is no simple way to calculate the perimeter of an ellipse. In this expository paper we review and compare four methods of evaluating this perimeter. These methods are known by the names Maclaurin, Gauss-Kummer, Cayley, and Euler. Maclaurin's method is derived in detail, while the other three are simply described. A short introduction to hypergeometric functions is included, since these functions are useful for finding the elliptic perimeter. We compare the usefulness of these four calculations, An appendix gives MICROSOFT EXCEL® programs for computing the perimeter.