Improved understanding of the molecular underpinnings of cancer initiation and progression has led to the development of targeted cancer therapies. The importance of these new methods of cancer treatment necessitates further research into the dynamic interactions between cancer cells and therapeutic agents, as well as a means of analysing their relationship quantitatively. The present review outlines the application of mathematical modelling to the dynamics of targeted cancer therapy, focusing particular attention on chronic myeloid leukaemia and its treatment with imatinib (Glivec).