Vervet monkeys (genus Chlorocebus, also known as African green monkeys), are highly abundant in savannahs and riverine forests throughout sub-Saharan Africa. They are amongst the most widely distributed nonhuman primates, show considerable phenotypic diversity, and have long been an important biomedical model for a variety of human diseases and in vaccine research. They are particularly interesting for HIV/AIDS research as they are the most abundant natural hosts of simian immunodeficiency virus (SIV), a close relative of HIV. Here we present the first genome-wide survey of polymorphism in vervets, using sequencing data from 163 individuals sampled from across Africa and the Caribbean islands where vervets were introduced during the colonial era. We find high diversity, within and between taxa, and clear evidence that taxonomic divergence was reticulate rather than following a simple branching pattern. A scan for diversifying selection across vervet taxa yields gene enrichments much stronger than in similar studies on humans. In particular, we report strong and highly polygenic selection signals affecting viral processes --- in line with recent evidence that proposes a driving role for viruses in protein evolution in mammals. Furthermore, selection scores are highly elevated in genes whose human orthologs interact with HIV, and in genes that show a response to experimental SIV infection in vervet monkeys but not in rhesus macaques, suggesting that part of the signal reflects taxon-specific adaptation to SIV. Intriguingly, rather than affecting genes with antiviral and inflammatory-related functions, selection in vervets appears to have primarily targeted genes involved in the transcriptional regulation of viruses, and in particular those that are harmful only under immunodeficiency, suggesting adaptation to living with SIV rather than defense against infection.