Human papillomavirus (HPV) refers to a group of viruses which belongs to a larger group, commonly referred to as papillomaviruses. These viruses are taxonomically located in the Papillomaviridae family. Papillomaviruses are small, non-enveloped with a genome of double-stranded DNA and they have affinity for epithelial tissue. Many of them are associated with human infection; they induce benign lesions of the skin (warts) and mucous membranes (condylomas), but they are also associated with some epithelial malignancies, such as cervical cancer and other tumors of the urogenital tract. Papillomaviridae contains 16 genera, which are named with a Greek letter prefix and the termination papillomavirus, e.g., Alphapapillomavirus, Betapapillomavirus, etcetera. From the clinical point of view, human papillomaviruses infecting the genital tract (which are located in the genus Alphapapilomavirus) have been divided into two groups: those of low risk, associated with benign genital warts, and those of high risk, with oncogenic potential, which are the etiological agents of cervical cancer. In this paper we review some relevant aspects of the structure, replication cycle and classification of human papillomaviruses.