Mathematical models of cancer growth and evolution of cancer cell characteristics, aka traits or phenotypes, together with optimisation and optimal control methods to contain them, in the framework of adaptive dynamics of cell populations, are presented. They take into account the heterogeneity of cancer cell populations, i.e., their biological variability, and their intrinsic plasticity, i.e., their nongenetic instability that allows them to quickly adapt to changing environments. The presented vision of the cancer disease, which is specific to multicellular organisms, relies on a relatively novel vision, consistent with a billion-year evolutionary perspective. Based on recent contributions from philosophy of cancer, these mathematical models aim at designing theoretical therapeutic strategies to simultaneously contain tumour progression and limit adverse events of drugs to healthy cell populations.