The modelling of cancer provides an enormous mathematical challenge because of its vast complexity. Here we address a number of key problems in tumour growth: (a) homeostasis and progression to cancer in the colorectal crypt; (b) somatic evolution and metabolic effects in ductal carcinoma in situ; (c) vascular tumour growth and the effects of different therapeutic strategies. The models range from very simple systems of ordinary differential equations, to hybrid cellular automata.