Combination antiretroviral therapy (cART) has led to a very substantial reduction in morbidity and mortality in HIV‐infected patients; however, cART alone is unable to cure HIV and therapy is lifelong. Therefore, a new strategy to cure HIV is urgently needed. There is now a concerted effort from scientists, clinicians and funding agencies to identify ways to achieve either a functional cure (long‐term control of HIV in the absence of cART) or a sterilizing cure (elimination of all HIV‐infected cells). Multiple strategies aiming at achieving a cure for HIV are currently being investigated, including both pharmacotherapy and gene therapy. In this review, we will review the rationale as well as in vitro and clinical trial data that support the role of histone deacetylase inhibitors as one approach to cure HIV.