Replication-competent latent HIV-1 proviruses that persist in the genomes of a very small subset of resting memory T cells in infected individuals under life-long antiretroviral therapy present a major barrier towards viral eradication. Multiple molecular mechanisms are required to repress the viral trans-activating factor Tat and disrupt the regulatory Tat feedback circuit leading to the establishment of the latent viral reservoir. In particular, latency is due to a combination of transcriptional silencing of proviruses via host epigenetic mechanisms and restrictions on the expression of P-TEFb, an essential co-factor for Tat. Induction of latent proviruses in the presence of antiretroviral therapy is expected to enable clearance of latently infected cells by viral cytopathic effects and host antiviral immune responses. An in-depth comprehensive understanding of the molecular control of HIV-1 transcription should inform the development of optimal combinatorial reactivation strategies that are intended to purge the latent viral reservoir.