Ductal carcinoma in situ (DCIS) is a non-invasive breast neoplasia that accounts for 25% of all screen-detected breast cancers diagnosed annually. Neoplastic cells in DCIS are confined to the ductal system of the breast, although they can escape and progress to invasive breast cancer in a subset of patients. A key concern of DCIS is overtreatment, as most patients screened for DCIS and in whom DCIS is diagnosed will not go on to exhibit symptoms or die of breast cancer, even if left untreated. However, differentiating low-risk, indolent DCIS from potentially progressive DCIS remains challenging. In this Review, we summarize our current knowledge of DCIS and explore open questions about the basic biology of DCIS, including those regarding how genomic events in neoplastic cells and the surrounding microenvironment contribute to the progression of DCIS to invasive breast cancer. Further, we discuss what information will be needed to prevent overtreatment of indolent DCIS lesions without compromising adequate treatment for high-risk patients.