Non-human primate (NHP) models are important for vaccine development and also contribute to HIV cure research. Although none of the animal models are perfect, NHPs enable the exploration of important questions about tissue viral reservoirs and the development of intervention strategies. In this review, we describe recent advances in the use of these models for HIV cure research and highlight the progress that has been made as well as limitations using these models. The main NHP models used are (i) the macaque, in which simian immunodeficiency virus (SIVmac) infection displays similar replication profiles as to HIV in humans, and (ii) the macaque infected by a recombinant virus (SHIV) consisting of SIVmac expressing the HIV envelope gene serving for studies analyzing the impact of anti-HIV Env broadly neutralizing antibodies. Lessons for HIV cure that can be learned from studying the natural host of SIV are also presented here. An overview of the most promising and less well explored HIV cure strategies tested in NHP models will be given.