Ductal carcinoma in situ (DCIS)--a type of breast cancer whose growth is confined to the duct lumen--is a significant precursor to invasive breast carcinoma. DCIS is commonly detected as a subtle pattern of calcifications in mammograms. Radiologic imaging (including mammography) is used to plan surgical resection of the tumor (lumpectomy), but multiple surgeries are often required to fully eliminate DCIS. On the other hand, pathologists use pre-surgical biopsies to stage the DCIS, assess its metastatic potential, and choose adjuvant therapies. There is currently no technique to combine these data to improve surgical and therapeutic planning. Mechanistic, patient-tailored computational models may provide such a link between multiple data types. In this talk, we focus on developing and calibrating biologically-grounded mathematical models to individual patients, encouraging (and validated!) results in quantitatively predicting clinical progression, the implications for making and quantitatively testing biological hypotheses, and the role of mathematical modeling in facilitating a deeper understanding of pathology and mammography.