The goal of this article is to suggest that mathematical models describing biological processes taking place within a patient over time can be used to design adaptive treatment strategies. We demonstrate using the key example of treatment strategies for human immunodeficiency virus type-1 (HIV) infection. Although there has been considerable progress in management of HIV infection using highly active antiretroviral therapies, continuous treatment with these agents involves significant cost and burden, toxicities, development of drug resistance, and problems with adherence; these latter complications are of particular concern in substance-abusing individuals. This has inspired interest in structured or supervised treatment interruption (STI) strategies, which involve cycles of treatment withdrawal and re-initiation. We argue that the most promising STI strategies are adaptive treatment strategies. We then describe how biological mechanisms governing the interaction over time between HIV and a patient's immune system may be represented by mathematical models and how control methods applied to these models can be used to design adaptive STI strategies seeking to maintain long-term suppression of the virus. We advocate that, when such mathematical representations of processes underlying a disease or disorder are available, they can be an important tool for suggesting adaptive treatment strategies for clinical study.