Antiretroviral therapy (ART) controls viral replication and has dramatically improved the quality and life expectancy of people living with HIV (PLHIV). However, almost 40 years after the discovery of HIV, there is still no cure; even after years of effective ART, the virus persists in cells, primarily memory CD4 T cells. These cells are a perennial source of infectious viruses, which necessitate that people living with HIV continue ART for life. Research on HIV reservoirs over the past 25 years has provided insight into how some infected cells persist for decades without being cleared by ART nor by immune responses. HIV “hides” in cells with extended lifespans, which have the capacity to proliferate through diverse mechanisms and which preferentially express several receptors that allow them to remain invisible to the immune system. A better understanding of these mechanisms of persistence is a necessary prerequisite for the development of therapeutic strategies aimed at eradicating HIV.