Therapeutic resistance continues to be an indominable foe in our ambition for curative cancer treatment. Recent insights into the molecular determinants of acquired treatment resistance in the clinical and experimental setting have challenged the widely held view of sequential genetic evolution as the primary cause of resistance and brought into sharp focus a range of non-genetic adaptive mechanisms. Notably, the genetic landscape of the tumour and the non-genetic mechanisms used to escape therapy are frequently linked. Remarkably, whereas some oncogenic mutations allow the cancer cells to rapidly adapt their transcriptional and/or metabolic programme to meet and survive the therapeutic pressure, other oncogenic drivers convey an inherent cellular plasticity to the cancer cell enabling lineage switching and/or the evasion of anticancer immunosurveillance. The prevalence and diverse array of non-genetic resistance mechanisms pose a new challenge to the field that requires innovative strategies to monitor and counteract these adaptive processes. In this Perspective we discuss the key principles of non-genetic therapy resistance in cancer. We provide a perspective on the emerging data from clinical studies and sophisticated cancer models that have studied various non-genetic resistance pathways and highlight promising therapeutic avenues that may be used to negate and/or counteract the non-genetic adaptive pathways.