The identification of oncogenic driver mutations in non-small-cell lung cancer (NSCLC) has led to the development of targeted drugs. Tyrosine kinase inhibitors (TKIs) directed against the epidermal growth factor receptor (EGFR) target lung tumours bearing EGFR-activating mutations. This new therapeutic strategy has greatly improved tumour response rates. However, drug resistance invariably occurs during TKI-based treatment. Epithelial-to-mesenchymal transition (EMT) is one of the resistance mechanisms identified in EGFR-mutated NSCLC treated with TKIs. In this review we gather together the most important findings on this phenomenon in relation to cancer stem cells and cancer epigenetics. We also outline the correlation between the effects of stromal factors from the microenvironment, the transcription factors activated, the epigenetic changes in chromatin, and the evolution of cellular behaviour. Notably, EMT has already been shown to be the link between benign lung diseases such as chronic obstructive pulmonary disease and lung carcinogenesis. The various mechanisms of acquired resistance to EGFR-TKIs are also briefly described to provide background information on EMT. Our extensive review of the scientific literature serves to highlight the cellular and molecular events that lead to the onset of EMT in NSCLC cells treated with EGFR-TKIs. Finally, we put forward a hypothesis to explain why, in some cases, EMT rather than other known mechanisms is involved in resistance to TKIs.