The course of HIV infection is arrested by antiretroviral therapy (ART). However, life-long ART is undesirable. To eradicate infection, strategies are needed to deplete the rare population of proviral genomes that persist and reemerge if ART is interrupted. Proviral HIV persists due to the simultaneous deficiency of factors required to allow proviral expression and virion production, and a predominance of factors that obstruct proviral expression. Combining ART with global inducers of T-cell activation has so far failed to eradicate HIV infection. One approach to the selective removal of obstacles to proviral expression, inhibition of the chromatin remodeling enzyme histone deacetylase, has entered clinical testing. Additional approaches may be needed. Ultimately, therapies that eliminate rare cells that persistently express HIV and interrupt low levels of viremia that persist in some patients may be required to render depletion of proviral HIV infection clinically relevant, and lead to the clearance of HIV infection.