Combination antiretroviral therapy (cART) successfully prolongs the life of HIV+ patients, prevents the development of AIDS and substantially reduces the risk of HIV-1 transmission. However, cART is not curative and patients must adhere to a life-long cART regimen, leading to a new set of complications and making of HIV a chronic disease. Indeed, cessation of cART invariably leads to a rapid rebound of the virus in most patients. HIV-1 persistence is notably due to the existence of replication-competent, transcriptionally-silent proviruses in a latent state. Latently-infected cells, mainly resting CD4+ T cells but possibly other infected cell types, are insensitive to cART and can evade the patient immune system. However, latency is a reversible state and reactivation of HIV-1 gene expression from latently-infected cells constitutes a permanent source for virus production in cART-treated patients. One of the most explored therapeutic approach aiming at purging HIV-1 reservoirs, the shock and kill strategy, consists in reactivating HIV-1 gene expression from the latently-infected cellular reservoirs, followed by killing of the virus-producing infected cells. Several classes of latency reversing agents (LRAs), including epigenetic modifying agents, have been studied to reactivate viral gene expression, based on the understanding of the molecular mechanisms involved in HIV-1 latency. Due to the small numbers of latently-infected cells found in vivo, these molecular mechanisms have been mainly studied in in vitro cell line and primary cell models for HIV-1 latency and in ex vivo models obtained with patient-derived latently-infected cells. However, many of these studies have highlighted the major contribution of epigenetic and transcriptional mechanisms to HIV-1 silencing. Clinical trials using individual LRAs have yielded variable, but sometimes encouraging results concerning their ability to induce HIV-1 transcription. However, none of these trials have caused significant and persistent reduction in the HIV-1 reservoir size. The multiplicity of the silencing mechanisms involved in HIV-1 latency, the intrinsically dynamic and heterogeneous nature of the latent HIV-1 cellular reservoirs, the variations in patient clinical history and the lack of selectivity of LRAs constitute causes of the LRA ineffectiveness in clinical trials. These causes will need to be understood in order to rationally improve the “shock” strategy so that it could reach clinical success.