The available evidence suggests that cancer is essentially a somatic evolutionary process involving a series of mutations. Each mutation gives some advantage to a selected clone, and expansion then occurs within that selected clone. The advantages are associated with both growth rate and factors leading to independent growth. The aim of this paper is first to give some background information on genetic changes in tumours, using colorectal cancer as an example. We will then introduce a mathematical model that explains many phenomena associated with the development of benign tumours and the long lag periods that are characteristic of the development of human tumours. The model addresses populations of cells and not populations of people.