The introduction of the highly active antiretroviral therapy (HAART) has greatly improved survival. However, these treatments fail to definitively cure the patients and unveil the presence of quiescent HIV-1 reservoirs like cells from monocyte-macrophage lineage. A purge, or at least a significant reduction of these long lived HIV-1 reservoirs will be needed to raise the hope of the viral eradication. This review focuses on the molecular mechanisms responsible for viral persistence in cells of the monocyte-macrophage lineage. Controversy on latency and/or cryptic chronic replication will be specifically evoked. In addition, since HIV-1 infected monocyte-macrophage cells appear to be more resistant to apoptosis, this obstacle to the viral eradication will be discussed. Understanding the intimate mechanisms of HIV-1 persistence is a prerequisite to devise new and original therapies aiming to achieve viral eradication.