The success of targeted therapies in cancer treatment has been impeded by various mechanisms of resistance. Besides the acquisition of resistance-conferring genetic mutations, reversible mechanisms that lead to drug tolerance have emerged. Plasticity in tumour cells drives their transformation towards a phenotypic state that no longer depends on the drug-targeted pathway. These drug-refractory cells constitute a pool of slow-cycling cells that can either regain drug sensitivity upon treatment discontinuation or acquire permanent resistance to therapy and drive relapse. In the past few years, cell plasticity has emerged as a mode of targeted therapy evasion in various cancers, ranging from prostate and lung adenocarcinoma to melanoma and basal cell carcinoma. Our understanding of the mechanisms that control this phenotypic switch has also expanded, revealing the crucial role of reprogramming factors and chromatin remodelling. Further deciphering the molecular basis of tumour cell plasticity has the potential to contribute to new therapeutic strategies which, combined with existing anticancer treatments, could lead to deeper and longer-lasting clinical responses.