Combinatory antiretroviral therapy (cART) reduces human immunodeficiency virus type 1 (HIV-1) replication but is not curative because cART interruption almost invariably leads to a rapid rebound of viremia due to the persistence of stable HIV-1-infected cellular reservoirs. These reservoirs are mainly composed of CD4+ T cells harboring replication-competent latent proviruses. A broadly explored approach to reduce the HIV-1 reservoir size, the shock and kill strategy, consists of reactivating HIV-1 gene expression from the latently infected cellular reservoirs (the shock), followed by killing of the virus-producing infected cells (the kill). Based on improved understanding of the multiple molecular mechanisms controlling HIV-1 latency, distinct classes of latency reversing agents (LRAs) have been studied for their efficiency to reactivate viral gene expression in in vitro and ex vivo cell models. Here, we provide an up-to-date review of these different mechanistic classes of LRAs and discuss optimizations of the shock strategy by combining several LRAs simultaneously or sequentially.