The invention provides compositions and methods for treating human papillomavirus (HPV) infections using a targetable nuclease, which compositions and methods can be used to selectively target the HPV genome or selectively express the targetable nuclease within cells that infected by HPV. By selectively targeting cells infected by HPV, the HPV genome within infected cells, or both, the nuclease is able to cleave the HPV genome thereby inactivating it and rendering it inoperable, interfering with the viruss ability to propagate even where the virus is in a latent stage of infection. Since latent HPV can be cleaved and eradicated from the host cells, compositions and methods of the invention may be used to treat HPV infections and potentially prevent many of the adverse health consequences associated with the papillomavirus.