A pool of latently infected CD4+ T cells is established within the first few weeks of HIV infection. Because these memory T cells are inactive, the viral DNA integrated into their chromosomes remains invisible to immune surveillance and to antiretrovirals. Research shows that this reservoir of infected memory T cells does not decay in a clinically meaningful time frame--that is, within 60 years--in patients being treated with potent combination antiretrovirals. Even a hypothetical regimen that prevents any new infection of cells would not hasten the decay of this latent reservoir. Treatments that activate this reservoir have been studied in patients with suppressed viremia, but such interventions are highly toxic and have not succeeded so far. Studying rare individuals who manage to control activation of these latent cells may provide important clues to long-term control of HIV infection.