Despite the huge clinical success of antiretroviral therapy, several factors such as side effects, requirement of life-long adherence, high cost, incomplete access to therapies and development of drug resistance make the quest for an ultimate cure of HIV/AIDS a worldwide priority of biomedical research. In this respect, several sterilizing or functional cures have been reported in the last years in both non-human primates and humans. This review provides a summary of the main results achieved so far, outlining their strengths as well as their limitations. A synthetic interpretation of these results could be pivotal in order to develop an effective and widely available cure.