Combination antiretroviral therapy (cART) has led to a major reduction in HIV-related mortality and morbidity; however, HIV can still not be cured. Achieving either a functional cure (long-term control of HIV in the absence of cART) or a sterilizing cure (elimination of all HIV-infected cells) remains a major challenge. The most significant barrier to cure is the establishment of a latent or 'silent' infection in resting CD4 T cells. Several randomized clinical trials have demonstrated that treatment intensification with additional antiretrovirals has little impact on latent reservoirs. Some potential other approaches that may reduce the latent reservoir include very early initiation of cART and the use of agents that could reverse latent infection. Drugs such as histone deacetylase inhibitors, currently used and licensed for the treatment of some cancers; methylation inhibitors; cytokines such as IL-7 or activators of nuclear factor kappa B (NF-κB) such as prostratin, show promising activity in reversing latency in vitro when used either alone or in combination. Alternate strategies include using gene therapy to modify expression of CCR5 and therefore make cells resistant to HIV. This review will primarily focus on the advantages and disadvantages of methods currently being used to quantify persistent virus ex vivo in patients receiving cART and strategies aimed at cure that are being tested in vitro or in early clinical development. In addition, we discuss key issues that need to be addressed to successfully move laboratory research to clinical trials aimed at curing HIV.