Human papillomavirus (HPV) causes virtually all cervical cancers and many cancers at other anatomical sites in both men and women. However, only 12 of 448 known HPV types are currently classified as carcinogens, and even the most carcinogenic type — HPV16 — only rarely leads to cancer. HPV is therefore necessary but insufficient for cervical cancer, with other contributing factors including host and viral genetics. Over the last decade, HPV whole genome sequencing has established that even fine-scale within-type HPV variation influences precancer/cancer risks, and that these risks vary by histology and host race/ethnicity. In this review, we place these findings in the context of the HPV life cycle and evolution at various levels of viral diversity: between-type, within-type, and within-host. We also discuss key concepts necessary for interpreting HPV genomic data, including features of the viral genome; events leading to carcinogenesis; the role of APOBEC3 in HPV infection and evolution; and methodologies that use deep (high-coverage) sequencing to characterize within-host variation, as opposed to relying on a single representative (consensus) sequence. Given the continued high burden of HPV-associated cancers, understanding HPV carcinogenicity remains important for better understanding, preventing, and treating cancers attributable to infection.