9 years since the report of a cure for HIV after C-C chemokine receptor type 5 Δ32 stem cell transplantation, no other case of HIV cure has been reported, despite much research. However, substantial progress has been made in understanding the biology of the latent HIV reservoir, and in measuring the amount of virus that persists after antiretroviral therapy (ART) with increasingly sophisticated approaches. This knowledge is being translated into a long pipeline of clinical trials seeking to reduce viral persistence in participants on suppressive treatment and ultimately to allow safe cessation of ART. In this Review, we discuss the main barriers preventing the development of an HIV cure, methods used to measure HIV persistence in individuals on ART, clinical strategies that aim to cure HIV, and future directions for studies in the field of HIV cure research.