BACKGROUND: In 2008, researchers reported that Timothy Brown (the 'Berlin Patient'), a man with HIV infection and leukemia, received a stem-cell transplant that removed HIV from his body as far as can be detected. In 2013, an infant born with HIV infection received anti-retroviral treatment shortly after birth, but was then lost to the health care system for the next six months. When tested for HIV upon return, the child (the 'Mississippi Baby') had no detectable viral load despite cessation of treatment. These remarkable clinical developments have helped reinvigorate the field of 'HIV cure' research. DISCUSSION: Although this research field is largely in a pre-clinical phase, talk about curing HIV has become a regular feature in the global mass media. This paper explores the language of HIV cure from philosophical, ethical and historical perspectives. Examination of currently influential definitions of 'functional' and 'sterilizing' HIV cure reveal that these conceptualizations are more complicated than they seem. Cure is often understood in narrowly biomedical terms in isolation from the social and psychological dimensions of illness. Contemporary notions of HIV cure also inherit some of the epistemic problems traditionally associated with cures for other health conditions, such as cancer. Efforts to gain greater conceptual clarity about cure lead to the normative question of how 'HIV cure research' ought to be talked about. SUMMARY: We argue that attention to basic concepts ethically matter in this context, and identify advantages as well as potential pitfalls of how different HIV/AIDS stakeholders may make use of the concept of cure. While concepts other than cure (such as remission) may be appropriate in clinical contexts, use of the word cure may be justified for other important purposes in the struggle against HIV/AIDS.