Carcinogenesis, at least for some types of cancer, can be interpreted as the consequence of selection of mutated cells similar to what, in the theory of evolution, occurs at the population level. Instead of considering a population of organisms, we can refer to a population of cells belonging to multicellular organisms. Many carcinogens are mutagens, and the observed geographic distribution of cancer is, at least in part, attributable to environmental mutagens. However, the rapid change in risk for some cancers after migration suggests that carcinogenesis involves--in addition to mutations--some late event that most probably consists of the selection of cells already carrying mutations. We review a few examples of such selective pressures: finasteride in prostate cancer, vitamin supplementation in smokers, acquired resistance to chemotherapy, peripheral resistance to insulin, and sunlight and mutations in melanoma. A disease model for such a hypothesis is represented by Paroxysmal Nocturnal Hemoglobinuria (PNH). Mutations can be present at birth, as in the case of PNH, and can have a frequency much higher than the occurrence of the corresponding disease (PNH or lymphocytic leukaemia in children). However, PNH does not require a mutator phenotype, only a mutant phenotype followed by selection. A characteristic feature of cancer, instead, is likely to be the development of the mutator phenotype. We propose a 'Darwinian' model of carcinogenesis. If the model is correct, it suggests that prevention is more complex than avoiding exposure to mutagens. Mutations and genetic instability can be already present at birth. Mutations can be selected in the course of life if they increase survival advantage of the cell under certain environmental circumstances. In addition, gene-environment interactions cannot be interpreted according to a simplified linear model (based on the 'analysis of variance' concept); experimental work suggests that a more comprehensive non-linear interpretation based on the idea of 'norm of reaction' is needed.