The necessity of separating DNA molecules according to size arises in numerous steps of molecular genetics research. It is usually accomplished by the electrically driven migration of the charged DNA molecules in a gel. The mobility in such conditions displays rather complicated features; it depends on both the field strength and the field history (the basis of the powerful ‘pulsed field electrophoresis’ techniques) and, in some circumstances, may be strongly non-monotonic as a function of size. The microscopic motion of DNA that leads to this behaviour has been investigated by a number of different approaches, including analytic theory, computer simulation, spectroscopic study of molecular orientation and observation of individual, labelled DNA molecules by means of fluorescence videomicroscopy. Several mechanisms of migration have been identified: reptation, in which the linear DNA molecule threads its way head-on through the pores of the gel, is the underlying mode of motion in most situations; more complicated behaviour, such as the formation of multiple loops (or ‘hernias’) and molecular trapping, are also observed in certain circumstances. The present state of understanding of this challenging field is reviewed and the implications of recent discoveries for practical applications are discussed.