Pancreatic ductal adenocarcinoma (PDAC) is one of the five most lethal malignancies worldwide and survival has not improved substantially in the past 30 years. Desmoplasia (abundant fibrotic stroma) is a typical feature of PDAC in humans, and stromal activation commonly starts around precancerous lesions. It is becoming clear that this stromal tissue is not a bystander in disease progression. Cancer–stroma interactions effect tumorigenesis, angiogenesis, therapy resistance and possibly the metastatic spread of tumour cells. Therefore, targeting the tumour stroma, in combination with chemotherapy, is a promising new option for the treatment of PDAC. In this Review, we focus on four issues. First, how can stromal activity be used to detect early steps of pancreatic carcinogenesis? Second, what is the effect of perpetual pancreatic stellate cell activity on angiogenesis and tissue perfusion? Third, what are the (experimental) antifibrotic therapy options in PDAC? Fourth, what lessons can be learned from Langton's Ant (a simple mathematical model) regarding the unpredictability of genetically engineered mouse models?