Today, HIVâ1 infection maintains its status as a grave public health problem. The development of effective antiretroviral drugs has greatly increased life expectancy of infected patients by arresting disease progression, but treatment is not able to eliminate the virus from the body, requiring lifelong adherence to prevent viral rebound and its consequent damage on the host immune system. The ability of the virus to remain latent in cellular reservoirs is a major obstacle in the development of curative therapies, in part because there is still a considerable lack of understanding of viral latency processes. A lot of research has been conducted to study and clarify such mechanisms and propose strategies to eradicate the virus (sterilising cure) or at least permanently control it (functional cure) in order to bypass the need for chronic antiretroviral therapy. The purpose of this literature review is to discuss the state of the art in HIVâ1 research, with a particular focus on the mechanisms by which HIVâ1 eradication has thus far remained an unattainable goal. Future perspectives for the development of a functional or sterilising cure to HIVâ1 infection will also be explored.