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Technological advances in genome sequencing and copy number analysis have allowed researchers to catalog the wide variety of genomic alterations that occur across diverse cancer types. For most cancer types, the lack of high-frequency alterations and the heterogeneity observed both within and between tumors suggest neoplastic progression proceeds through a branched evolutionary pathway as proposed by Nowell in 1976, as opposed to the linear pathway that has dominated medical science for the last century. To understand how cancer evolves over time and space in the body, new study designs are needed that can distinguish between alterations that develop in patients who progress to cancer from to those who don't. Here we present approaches developed in the study of Barrett's esophagus, a premalignant precursor of esophageal adenocarcinoma, and discuss strategies for applying the results from these analyses to address the critical clinical problems of overdiagnosis of benign disease, early detection of life-threatening cancer, and effective risk stratification.