Current anti-retroviral treatment (ART) for HIV-1 is highly effectively at controlling the infection. However, during early infection the virus establishes a latent reservoir, which is not impacted by ART. Any treatment interruption rapidly results in virus rebound from the latent reservoir to pre-therapy levels and thus ART does not constitute an HIV-1 cure. Alternate treatments are currently being explored in the form of gene therapy, following the success of the Berlin patient who has had undetectable virus since 2007. This review will describe the contrasting cure approaches that are currently the focus of multiple studies to control HIV, then focus in on functional cure gene therapy strategies; specifically, epigenetic silencing of HIV-1 by various methods, including RNA-directed transcriptional gene silencing. The various delivery strategies for targeting cells of the latent reservoir will be reviewed and finally, the clinical status and current challenges for ex vivo versus in vivo gene therapy delivery approaches will be discussed.