HIV-1/AIDS remains a global public health problem. The world health organization (WHO) reported at the end of 2019 that 38 million people were living with HIV-1 worldwide, of which only 67% were accessing antiretroviral therapy (ART). Despite great success in the clinical management of HIV-1 infection, ART does not eliminate the virus from the host genome. Instead, HIV-1 remains latent as a viral reservoir in any tissue containing resting memory CD4⁺ T cells. The elimination of these residual proviruses that can reseed full-blown infection upon treatment interruption remains the major barrier towards curing HIV-1. Novel approaches have recently been developed to excise or disrupt the virus from the host cells (e.g., gene editing with the CRISPR-Cas system) to permanently shut off transcription of the virus (block-and-lock and RNA interference strategies), or to reactivate the virus from cell reservoirs so that it can be eliminated by the immune system or cytopathic effects (shock-and-kill strategy). Here, we will review each of these approaches, with the major focus placed on the block-and-lock strategy.