The landscape of Human Immunodeficiency Virus (HIV) research has changed drastically over the past three decades. With the remarkable success of antiretroviral treatment (ART) in decreasing AIDS-related mortality, some researchers have shifted their HIV research focus from treatment to cure research. The HIV cure research community often uses the term eradication to describe the science, and talks about eradicating the virus from the body. In public discourse, the term eradication could be conflated with disease eradication at the population level. In this paper, we call for a reframing of HIV cure research as control, as it is a more accurate descriptor and achievable goal in the foreseeable future.The properties of HIV are discordant with eradicability standards at both the individual level (as a clinical concept), and at the population level (as a public health concept). At the individual level, true eradication would necessitate absolute elimination of all latent HIV reservoirs from the body. Current HIV cure-related research strategies have proven unsuccessful at accurately quantifying, let alone eliminating these reservoirs. At the population level, eradication implies the permanent global reduction of HIV to zero new cases and to zero risk for future cases. Given the absence of an efficacious HIV vaccine and the impracticality and unethicality of eliminating animal reservoirs, global eradication of HIV is highly implausible. From a public health perspective, HIV eradication remains an elusive goal.The term 'eradication' is a misleading description of current HIV cure-related research. Instead, we call for the use of more realistic expressions such as 'sustained virologic HIV suppression (or control)' or 'management of HIV persistence' to describe HIV cure-related research. Using these terms reorients what HIV cure science can potentially achieve in the near future and avoids creating unrealistic expectations, particularly among the millions of people globally who live with HIV.