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 very general types of evolutionary patterns, loss-of-function and gain-of-function mutations, both of which are commonly observed in many cancers. I will discuss several scenarios of population dynamics, including stochastic tunneling and calculating the rate of evolution, and show how the rate if evolution depends on the underlying cell dynamics (such as spatial interactions and a hierarchical structure of the population). I will apply the theory to the case of colorectal cancer progression, which includes both an inactivation of a tumor suppressor gene (a loss-of-function event) and an activation of an oncogene (a gain-of-function event). I will show how the microscopic dynamics in a colonic crypt is directly connected with cancer epidemiology, and specifically focus on the role of aspirin in colorectal cancer prevention. I will demonstrate how the model can be parametrized based on in vivo and in vitro measurements performed by experimental collaborators, under varying doses of aspirin. This type of modeling can be used to study the poorly understood mechanisms of cancer risk reduction by aspirin.