Bornaviruses are the only animal RNA viruses that establish a persistent infection in their host cell nucleus. Studies of bornaviruses have provided unique information about viral replication strategies and virus–host interactions. Although bornaviruses do not integrate into the host genome during their replication cycle, we and others have recently reported that there are DNA sequences derived from the mRNAs of ancient bornaviruses in the genomes of vertebrates, including humans, and these have been designated endogenous borna-like (EBL) elements. Therefore, bornaviruses have been interacting with their hosts as driving forces in the evolution of host genomes in a previously unexpected way. Studies of EBL elements have provided new models for virology, evolutionary biology and general cell biology. In this review, we summarize the data on EBL elements including what we have newly identified in eukaryotes genomes, and discuss the biological significance of EBL elements, with a focus on EBL nucleoprotein elements in mammalian genomes. Surprisingly, EBL elements were detected in the genomes of invertebrates, suggesting that the host range of bornaviruses may be much wider than previously thought. We also review our new data on non-retroviral integration of Borna disease virus.