Human immunodeficiency virus type 1 (HIV-1) infection persists despite years of antiretroviral therapy (ART). To remove the stigma and burden of chronic infection, approaches to eradicate or cure HIV infection are desired. Attempts to augment ART with therapies that reverse viral latency, paired with immunotherapies to clear infection, have advanced into the clinic, but the field is still in its infancy. We review foundational studies and highlight new insights in HIV cure research. Together with advances in ART delivery and HIV prevention strategies, future therapies that clear HIV infection may relieve society of the affliction of the HIV pandemic.