Nonhuman primate (NHP) models of AIDS represent a potentially powerful component of the effort to understand in vivo sources of AIDS virus that persist in the setting of suppressive combination antiretroviral therapy (cART) and to develop and evaluate novel strategies for more definitive treatment of HIV infection (i.e., viral eradication “cure”, or sustained off-cART remission). Multiple different NHP models are available, each characterized by a particular NHP species, infecting virus, and cART regimen, and each with a distinct capacity to recapitulate different aspects of HIV infection. Given these different biological characteristics, and their associated strengths and limitations, different models may be preferred to address different questions pertaining to virus persistence and cure research, or to evaluate different candidate intervention approaches. Recent developments in improved cART regimens for use in NHPs, new viruses, a wider array of sensitive virologic assay approaches, and a better understanding of pathogenesis should allow even greater contributions from NHP models to this important area of HIV research in the future.