Mathematical models have become an increasingly valuable tool in HIV research. In particular, the mathematical analysis of drug-induced perturbations of the steady-state viral load in chronically infected patients has led to fundamental new insights into HIV dynamics in vivo and demonstrated that there is highly active viral replication throughout the course of infection. The same models can be used to address issues related to drug resistance and may eventually provide theoretical guidelines for the design of efficient treatment strategies. The goal of this article is to illustrate to a readership with nonmathematical background how these models work, what key assumptions they make, and which questions they may help to answer.