Beginning in the 1980s, an alarming rise in the incidence of esophageal adenocarcinoma (EA) led to screening of patients with reflux to detect Barrett’s esophagus (BE) and surveillance of BE to detect early EA. This strategy, based on linear progression disease models, resulted in selective detection of BE that does not progress to EA over a lifetime (overdiagnosis) and missed BE that rapidly progresses to EA (underdiagnosis). Here we review the historical thought processes that resulted in this undesired outcome and the transformation in our understanding of genetic and evolutionary principles governing neoplastic progression that has come from application of modern genomic technologies to cancers and their precursors.