HIV-1 infection can now be readily controlled with combination antiretroviral therapy. However, the virus persists indefinitely in a stable latent reservoir in resting CD4+ T cells. This reservoir generally prevents cure of the infection with combination antiretroviral therapy alone. However, several recent cases of potential HIV-1 cure have generated renewed optimism. Here we review these cases and consider new developments in our understanding of the latent reservoir. In addition, we consider clinical aspects of curative strategies to provide a more realistic picture of what a generally applicable cure for HIV-1 infection is likely to entail.