Effective antiretroviral therapy (ART) blunts viraemia, which enables HIV-1-infected individuals to control infection and live long, productive lives. However, HIV-1 infection remains incurable owing to the persistence of a viral reservoir that harbours integrated provirus within host cellular DNA. This latent infection is unaffected by ART and hidden from the immune system. Recent studies have focused on the development of therapies to disrupt latency. These efforts unmasked residual viral genomes and highlighted the need to enable the clearance of latently infected cells, perhaps via old and new strategies that improve the HIV-1-specific immune response. In this Review, we explore new approaches to eradicate established HIV-1 infection and avoid the burden of lifelong ART.