Antiretroviral therapy reduces circulating HIV-1 to undetectable amounts but does not eliminate the virus due to the persistence of a stable reservoir of latently infected cells. The reservoir is maintained both by proliferation of latently infected cells and by reseeding from reactivated cells. A major challenge for the field is to find safe and effective methods to eliminate this source of rebounding HIV-1. Studies on the molecular mechanisms leading to HIV-1 latency and reactivation are being transformed using latency models in primary and patient CD4⁺ T cells. These studies have revealed the central role played by the biogenesis of the transcription elongation factor P-TEFb (Positive Transcription Elongation Factor b) and its recruitment to proviral HIV-1, for the maintenance of viral latency and the control of viral reactivation.