Cancer has long been viewed as a genetic disease of cumulative mutations. This notion is fuelled by studies showing that ageing tissues are often riddled with clones of complex oncogenic backgrounds coexisting in seeming harmony with their normal tissue counterparts. Equally puzzling, however, is how cancer cells harbouring high mutational burden contribute to normal, tumour-free mice when allowed to develop within the confines of healthy embryos. Conversely, recent evidence suggests that adult tissue cells expressing only one or a few oncogenes can, in some contexts, generate tumours exhibiting many of the features of a malignant, invasive cancer. These disparate observations are difficult to reconcile without invoking environmental cues triggering epigenetic changes that can either dampen or drive malignant transformation. In this Review, we focus on how certain oncogenes can launch a two-way dialogue of miscommunication between a stem cell and its environment that can rewire downstream events non-genetically and skew the morphogenetic course of the tissue. We review the cells and molecules of and the physical forces acting in the resulting tumour microenvironments that can profoundly affect the behaviours of transformed cells. Finally, we discuss possible explanations for the remarkable diversity in the relative importance of mutational burden versus tumour microenvironment and its clinical relevance.