Unified theories predict that the Universe passes through a sequence of phase transitions as it cools after the big bang. Topological structures (domain walls, strings and monopoles) may be created in these transitions. The production of domains of different zero-temperature vacua (separately by massive walls) excludes some popular scenarios for the breaking of SU(5) and SO(10). Massive strings appear in other schemes. They may be open strings or closed loops. We exhibit an SO(10) example with string formation. SO(8) supergravity may deliver an effective SU(5)× SU(2) unified theory below the Planck mass scale. This can also lead to string production. We present the rather restrictive conditions under which string producing theories are harmless to conventional cosmology. Even then, strings do not seem to provide the initial density perturbations that evolved into galaxies.