eco-evolutionary dynamics are at the core of carcinogenesis. mathematical methods can be used to study ecological and evolutionary processes, and to shed light into cancer origins, progression, and mechanisms of treatment. i will present two broad approaches to cancer modeling that we have developed. one is concerned with near-equilibrium dynamics of stem cells, with the goal of figuring out how tissue cell turnover is orchestrated, and how control networks prevent “selfish” cell growth. the other direction is studying evolutionary dynamics in random environments.  the presence of temporal or spatial randomness significantly affects the competition dynamics in populations and gives rise to some counterintuitive observations. applications to biomedical problems will be discussed.