The introduction in 1996 of the HAART raised hopes for the eradication of HIV-1. Unfortunately, the discovery of latent HIV-1 reservoirs in CD4+ T cells and in the monocyte-macrophage lineage proved the optimism to be premature. The long-lived HIV-1 reservoirs constitute a major obstacle to the eradication of HIV-1. In this review, we focus on the establishment and maintenance of HIV-1 latency in the two major targets for HIV-1: the CD4+ T cells and the monocyte-macrophage lineage. Understanding the cell-type molecular mechanisms of establishment, maintenance, and reactivation of HIV-1 latency in these reservoirs is crucial for efficient therapeutic intervention. A complete viral eradication, the holy graal for clinicians, might be achieved...