An open question amongst papillomavirus taxonomists is whether recombination has featured in the evolutionary history of these viruses. Since the onset of the global AIDS epidemic, the question is somewhat less academic, because immune-compromised human immunodeficiency virus patients are often co-infected with extraordinarily diverse mixtures of human papillomavirus (HPV) types. It is expected that these conditions may facilitate the emergence of HPV recombinants, some of which might have novel pathogenic properties. Here, a range of rigorous analyses is applied to full-genome sequences of papillomaviruses to provide convincing statistical and phylogenetic evidence that evolutionarily relevant papillomavirus recombination can occur.