Despite effective antiretroviral therapy (ART) and undetectable HIV RNA in the plasma, latent replication-competent HIV persists indefinitely in long-lived cells. Cessation of ART results in rebound of HIV from these persistent reservoirs. While this was thought to be an insurmountable obstacle to viral eradication, recent cases suggest otherwise. To date one patient has been "cured" of HIV and several others have been able to interrupt ART without viral rebound for prolonged periods. These events have sparked renewed interest in developing strategies that will allow eradication of HIV in infected individuals. We review the current knowledge of HIV latency and the viral reservoir, describe the potential utility of emerging cancer therapeutics in HIV cure research with an emphasis on pathways implicated in reservoir persistence, and outline opportunities and challenges in the context of the current clinical trial and regulatory environment.