Small molecule inhibitors target specific metabolic pathways in tumor cells and are a promising class of drugs for the treatment of cancers. The best known example is the treatment of chronic myeloid leukemia (CML) with Gleevec. This is a small molecule inhibitor of the Bcr-Abl kinase which has been shown to drive the initiation and progression of CML. While treatment of early stage CML with Gleevec has been quite successful, later stages of the disease (blast crisis) are not successfully treated due to the emergence of drug resistant cells. It is therefore important to understand the principles according to which drug resistant cells evolve, so that we can design treatment strategies which aim to prevent the rise of resistant cells. Such evolutionary dynamics can be studied with mathematical models, and this article reviews such an approach. We address three specific questions: (i) Do resistant cells emerge before or after the start of therapy? (ii) How does the turnover rate of cancer cells influence the evolution of drug resistant cells? (iii) Can combination therapy be used to prevent drug resistance? We apply our model to the treatment of CML with Gleevec, in order to demonstrate how this mathematical framework can be applied to the treatment of a specific cancer with small molecule inhibitors.