HIV-1 infection is characterized by a continuous viral replication throughout the illness that can be controlled to some extent by effective treatment. Early during primary infection, latent reservoirs where the virus remains hidden in metabolically inert cells are established. These reservoirs are responsible for a low-rate viral replication that can be observed even during effective treatment and are a major obstacle for the complete eradication of the infection. This low-rate viral replication also comes from anatomical sites where drug penetration is limited and only a suboptimal drug concentration can be achieved. Further understanding of the mechanisms underlying HIV-1 latency is of primary importance to develop new strategies that ensure the complete destruction of reservoirs and, therefore, the eradication of the infection.