The cancer genome is shaped by three components of the evolutionary process: mutation, selection and drift. While many studies have focused on the first two of these evolutionary components, the role of drift in cancer evolution has received little attention. Drift occurs when all individuals in the population have the same likelihood of producing surviving offspring, and so by definition a drifting population is one that is evolving neutrally. Here we focus on how neutral evolution is manifested in the cancer genome. We discuss how neutral passenger mutations provide a magnifying glass that reveals the evolutionary dynamics underpinning cancer development, and outline how statistical inference can be used to quantify these dynamics from sequencing data. We argue that only after we understand the impact of neutral drift on the genome can we begin to make full sense of clonal selection. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.