In patients with pancreatic ductal adenocarcinoma (PDAC), intratumoural and intertumoural heterogeneity increases chemoresistance and mortality rates. However, such morphological and phenotypic diversities are not typically captured by organoid models of PDAC. Here we show that branched organoids embedded in collagen gels can recapitulate the phenotypic landscape seen in murine and human PDAC, that the pronounced molecular and morphological intratumoural and intertumoural heterogeneity of organoids is governed by defined transcriptional programmes (notably, epithelial-to-mesenchymal plasticity), and that different organoid phenotypes represent distinct tumour-cell states with unique biological features in vivo. We also show that phenotype-specific therapeutic vulnerabilities and modes of treatment-induced phenotype reprogramming can be captured in phenotypic heterogeneity maps. Our methodology and analyses of tumour-cell heterogeneity in PDAC may guide the development of phenotype-targeted treatment strategies.