Electrophoresis of DNA through gels of agarose or polyacrylamide (PA) has been one of the most widely used techniques of molecular biology during the past decade, serving both analytical and preparative purposes. The molecular theory of this process has been developing slowly over the same period of time as the result of the efforts of a small but expanding group of people. Initially simple, the theory has grown in ways that no one anticipated at the beginning, partly in response to unexpected experimental discoveries. In this review we describe its current state, including both solved and unsolved problems.