Carcinogenesis is an evolutionary process; establishing the prognosis for a cancer therefore requires predicting the future course of cancer evolution. The same is true in pre-cancerous conditions: the risk of developing cancer is determined by how the pre-cancerous lesion is evolving. The level of heterogeneity within a population measures the evolvability of the population: if there is no diversity natural selection cannot operate, whereas diverse populations are likely to contain well-adapted individuals that can prosper in changing environments. Consequently, quantification of within-tumour heterogeneity is likely to be a proxy-measure of the rate of the underlying evolutionary process that drives carcinogenesis, and so be an effective prognostic marker. In this talk, I will describe how we have measured within-tumour diversity, both genetically and phenotypically, to successfully determine prognosis in both established cancers and in premalignant lesions. In addition, I will describe how we begun to search for the most prognostic measures of intra-tumour heterogeneity by constructing simple computational models of cancer development, and using the models to perform an exhaustive search of possible heterogeneity measures.