Our present theories of particle physics and cosmology, taken together, suggest that very early in its history, the universe underwent a series of phase transitions, at which topological defects, similar to those formed in some condensed matter transitions, may have been created. Such defects, in particular cosmic strings, may survive long enough to have important observable effects in the universe today. Predicting these effects requires us to estimate the initial defect density and the way that defects subsequently evolve. Very similar problems arise in condensed matter systems, and recently it has been possible to test some of our ideas about the formation of defects using experiments with liquid helium-3 (in collaboration with the Low Temperature Laboratory in Helsinki). I shall review the present status of this theory.