even though much progress has been made in mainstream experimental cancer research at the molecular level, traditional methodologies alone are sometimes insufficient to resolve important conceptual issues in cancer biology. in this talk, i will describe mathematical tools which help obtain new insights into the processes of cancer initiation, progression and treatment. the main idea is to study cancer as an evolutionary dynamical system on a selection-mutation network. i will discuss the following topics: stem cells and tissue architecture; stem cells and aging, and drug resistance in cml.