Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very early Universe. Certain types of defects lead to disastrous consequences for cosmology, others may play a useful role, as possible seeds for the formation of structure in the Universe, or in mediating baryon number violating processes. In all cases, topological defects lead to a fruitful interplay between particle physics and cosmology.

17 pages, no figures; Invited lectures at WHEPP-5, IUCAA, Pune, India, Jan. 12 - 26 1998