Epithelial–mesenchymal transition (EMT) is a cellular programme that is known to be crucial for embryogenesis, wound healing and malignant progression. During EMT, cell–cell and cell–extracellular matrix interactions are remodelled, which leads to the detachment of epithelial cells from each other and the underlying basement membrane, and a new transcriptional programme is activated to promote the mesenchymal fate. In the context of neoplasias, EMT confers on cancer cells increased tumour-initiating and metastatic potential and a greater resistance to elimination by several therapeutic regimens. In this Review, we discuss recent findings on the mechanisms and roles of EMT in normal and neoplastic tissues, and the cell-intrinsic signals that sustain expression of this programme. We also highlight how EMT gives rise to a variety of intermediate cell states between the epithelial and the mesenchymal state, which could function as cancer stem cells. In addition, we describe the contributions of the tumour microenvironment in inducing EMT and the effects of EMT on the immunobiology of carcinomas.