A small group of human papillomaviruses (HPVs) cause almost all cervical carcinoma and a significant percentage of other anogenital tract and oral carcinoma. Another group of HPVs causes non-melanoma skin cancers in genetically predisposed or immune suppressed patients upon UV exposure. HPV genome replication requires the host cell's DNA synthesis machinery and HPVs encode proteins that maintain differentiated epithelial cells in a replication competent state. The resulting rewiring of cellular signal transduction circuits triggers several innate cellular tumor suppressor responses that HPVs need to inactivate in order to establish persistent and/or productive infections. This review emphasizes this interplay between virus and the infected host cells and points out biological similarities and differences between different groups of HPVs.