Under the current standard of care, individuals with HIV take three antiretroviral drugs simultaneously. Triple-drug combination therapies limit HIV drug resistance evolution, because viruses resistant to a subset of the cocktail are suppressed by the remainder of the drugs and should not complete replication and spread. Despite this, reanalysis of HIV genetic data shortly after triple drug therapies became available (1990s and 2000s) reveals ongoing drug resistance in patients on three-drug therapies. In disagreement with expected patterns of evolution in three-drug therapy-treated HIV populations, resistance usually evolves one mutation at a time in a semi-predictable order. We argue here that these surprising observations can be explained using a model that divides the human body into compartments (for example, the gut, lymph nodes and brain). If one drug reaches a compartment that the other two drugs cannot, this creates a single-drug compartment that can select for single-drug resistant viruses. Such viruses can potentially become resistant to additional drugs, if they migrate to another compartment where a second drug is present, and so on. In addition to a compartment model, for some drug combinations, an alternative model of time-heterogeneity due to short half-lives combined with sub-optimal adherence could also explain the observations. We discuss how these lessons from HIV drug resistance evolution may be useful for other systems.