Highly active antiretroviral therapy (HAART) has limited the replication and spread of the human immunodeficiency virus (HIV). However, despite treatment, HIV infection persists in latently infected reservoirs, and once therapy is interrupted, viral replication rebounds quickly. Extensive efforts are being directed at eliminating these cell reservoirs. This feat can be achieved by reactivating latent HIV while administering drugs that prevent new rounds of infection and allow the immune system to clear the virus. However, current approaches to HIV eradication have not been effective. Moreover, as HIV latency is multifactorial, the significance of each of its molecular mechanisms is still under debate. Among these, transcriptional repression as a result of reduced levels and activity of the positive transcription elongation factor b (P-TEFb: CDK9/cyclin T) plays a significant role. Therefore, increasing levels of P-TEFb expression and activity is an excellent strategy to stimulate viral gene expression. This review summarizes the multiple steps that cause HIV to enter into latency. It positions the interplay between transcriptionally active and inactive host transcriptional activators and their viral partner Tat as valid targets for the development of new strategies to reactivate latent viral gene expression and eradicate HIV. Full article