Ductal carcinoma in situ (DCIS) is the most frequently diagnosed early‐stage breast cancer. Only a subset of patients progress to invasive ductal carcinoma (IDC), and this presents a formidable clinical challenge for determining which patients to treat aggressively and which patients to monitor without therapeutic intervention. Understanding the molecular and genomic basis of invasion has been difficult to study in DCIS cancers due to several technical obstacles, including low tumour cellularity, lack of fresh‐frozen tissues, and intratumour heterogeneity. In this review, we discuss the role of intratumour heterogeneity in the progression of DCIS to IDC in the context of three evolutionary models: independent lineages, evolutionary bottlenecks, and multiclonal invasion. We examine the evidence in support of these models and their relevance to the diagnosis and treatment of patients with DCIS. We also discuss how emerging technologies, such as single‐cell sequencing, STAR‐FISH, and imaging mass spectrometry, are likely to provide new insights into the evolution of this enigmatic disease. Copyright © 2016 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.