Current theories of particle physics lend to the unavoidable conclusio
n that there must have been several phase transitions in the early Uni
verse. Further, in the context of these theories, it is possible that
cosmological phase transitions would have produced topological defects
that may be roaming our heavens today. A finding of these fossils fro
m the early Universe would provide a direct confirmation of the therma
l history of the cosmos, insight into astrophysical phenomena, and vit
al information about particle physics. The elimination of unobserved t
opological defects provides important constraints on particle physics
and may also suggest novel cosmology. I describe some of the research
on cosmic topological defects and recent efforts to address cosmologic
al issues in condensed matter systems.