Recent studies have uncovered myriad viral sequences that are integrated or 'endogenized' in the genomes of various eukaryotes. Surprisingly, it appears that not just retroviruses but almost all types of viruses can become endogenous. We review how these genomic 'fossils' offer fresh insights into the origin, evolutionary dynamics and structural evolution of viruses, which are giving rise to the burgeoning field of palaeovirology. We also examine the multitude of ways through which endogenous viruses have influenced, for better or worse, the biology of their hosts. We argue that the conflict between hosts and viruses has led to the invention and diversification of molecular arsenals, which, in turn, promote the cellular co-option of endogenous viruses.