An informal survey is presented of the numerical computation of Schwarz-Christoffel maps (i.e., conformal maps from a disk in the complex plane to a polygon) and their applications in science and engineering. It is shown that many superficially different problems of conformal mapping and potential theory can be reduced to Schwarz-Christoffel maps and then solved by software such as the Fortran package SCPACK. This report, not for publication, is a reproduction of a 1989 technical report from the Department of Mathematics at the Massachusetts Institute of Technology.