To date, more than 400 types of human papillomavirus (HPV) have been identified. Despite the creation of effective prophylactic vaccines against the most common genital HPVs, the viruses remain among the most prevalent pathogens found in humans. According to WHO data, they are the cause of 5% of all cancers. Even more frequent are persistent and recurrent benign lesions such as genital and common warts. HPVs are resistant to many disinfectants and relatively unsusceptible to external conditions. There is still no drug available to inhibit viral replication, and treatment is based on removing lesions or stimulating the host immune system. This paper presents the systematics of HPV and the differences in HPV structure between different genetic types, lineages, and sublineages, based on the literature and GenBank data. We also present the pathogenesis of diseases caused by HPV, with a special focus on the role played by E6, E7, and other viral proteins in the development of benign and cancerous lesions. We discuss further prospects for the treatment of HPV infections, including, among others, substances that block the entry of HPV into cells, inhibitors of viral early proteins, and some substances of plant origin that inhibit viral replication, as well as new possibilities for therapeutic vaccines.