Abstract Antiretroviral therapy effectively controls human immunodeficiency virus (HIV) infection. However, a reservoir of latently infected cells persists under suppressive therapy, constituting a major barrier to an HIV cure. The block-and-lock approach to a functional cure aims at the transcriptional and epigenetic silencing of proviruses, blocking viral reactivation in the absence of therapy, preventing disease progression and transmission, despite the presence of detectable integrated proviruses. This approach has been put forward for exploration based on the activity of didehydro–cortistatin A, an inhibitor of the HIV transcriptional activator Tat. Here we review the mechanisms by which didehydro–cortistatin A inhibition of Tat’s feedback loop transcriptional amplification results in epigenetic silencing of the HIV promoter, and we discuss the benefits and limitations of the block-and-lock approach for an HIV cure.