We review some crucial aspects of drug therapy and viral resistance that have been investigated within the framework developed for the modelling of virus kinetics. First, we give a general overview on the use of mathematical models in the field of HIV research. We seek to identify the factors that determine the steady state virus load and show that stable reductions during antiviral therapy are difficult to explain within the standard model of virus dynamics. We discuss possible extensions that enable the models to account for the moderately reduced virus loads during non-suppressive treatment and argue that the residual viremia under suppressive treatment can probably be attributed to the survival of long-lived infected cells, rather than to new rounds of replication. Next, we address the emergence of resistance during suppressive therapy and demonstrate that the resistant virus is more likely to be present already at the start of treatment than to be generated during therapy. The appearance of resistance after a prolonged period of initial suppression indicates that drug efficacy is not continuously maintained over time. We investigate the potential risks and benefits of therapy interruptions. Considering the effect of recombination, we argue that it probably decelerates, rather than accelerates the evolution of multidrug-resistant virus. We also review state-of-the-art methods for the estimation of fitness, which is crucial to the understanding of the emergence of resistance during therapy or the re-emergence of wild type upon the cessation of therapy.