We propose that carcinogenesis requires tumour populations to surmount six distinct microenvironmental proliferation barriers that arise in the adaptive landscapes of normal and premalignant populations growing from epithelial surfaces. Somatic evolution of invasive cancer can then be viewed as a sequence of phenotypical adaptations to these barriers. The genotypical and phenotypical heterogeneity of cancer populations is explained by an equivalence principle in which multiple strategies can successfully adapt to the same barrier. This model provides a theoretical framework in which the diverse cancer genotypes and phenotypes can be understood according to their roles as adaptive strategies to overcome specific microenvironmental growth constraints.