A model for carcinogenesis is presented that provides a framework for understanding the roles of "spontaneous" events, hereditary factors, and environmental agents in human carcinogenesis and for interpreting experimental carcinogenesis. This model incorporates two features: a) transition of target stem cells into cancer cells via an intermediate stage in two irreversible steps, and b) growth and differentiation of normal target and intermediate cells. Cast in mathematical terms, the model can be fitted to age-specific incidence data on human cancers of both children and adults and can illuminate the relative importance of agents that affect transition rates, tissue growth, and tissue differentiation. This is illustrated by application of the model to a) the epidemiology of lung cancer with emphasis on the role of cigarette smoking and b) the epidemiology of breast cancer with emphasis on the roles of hormones, radiation, and hereditary. The nature of the two events and of the intermediate stage is considered in light of hereditary conditions that predispose to cancer in humans. The modes of action of radiation and chemicals in carcinogenesis are discussed, as are predictions based on the model and amenable to experimental verification.