Advances in the treatment of HIV infection have dramatically reduced the death rate from AIDS and improved the quality of life of many HIV-infected individuals. However, the possible long-term toxicity associated with antiretroviral therapy (ART), stigma and cost, all contribute to the necessity of finding a cure for HIV infection. In infected individuals taking ART, HIV persists in a small number of cells that can survive for the lifetime of the infected person. These persistently infected cells, usually referred as the 'reservoirs for HIV infection', are the main barriers to a cure. The diversity of the tissues and cellular types in which HIV persists, as well as the multiplicity of the molecular mechanisms contributing to HIV persistence, complicate the efforts to develop a safe, effective, and globally accessible cure for HIV. In this review, we summarise recent data that contribute to our understanding of HIV persistence during ART by addressing three questions pertaining to the HIV reservoir: (1) when is the reservoir established; (2) where is the reservoir maintained; and (3) how does the reservoir persist?