Human immunodeficiency virus infection is still one of the most important causes of morbidity and mortality in the world, with a disproportionate human and economic burden especially in poorer countries. Despite many years of intense research, an aspect that still is not well understood is what (immune) mechanisms control the viral load during the prolonged asymptomatic stage of infection. Because CD8+ T cells have been implicated in this control by multiple lines of evidence, there has been a focus on understanding the potential mechanisms of action of this immune effector population. One type of experiment used to this end has been depleting these cells with monoclonal antibodies in the simian immunodeficiency virus-macaque model and then studying the effect of that depletion on the viral dynamics. In this paper, we review what these experiments have told us. Finally, we emphasize modeling studies to interpret the changes in viral load observed in these experiments, including discussion of alternative models, assumptions and interpretations, as well as potential future experiments.