Epithelial mesenchymal transition (EMT) is a reversible developmental genetic programme of transdifferentiation of polarised epithelial cells to mesenchymal cells. In cancer, EMT is an important factor of tumour cell plasticity and has received increasing attention for its role in the resistance to conventional and targeted therapies. In this paper we provide an overview of EMT in human malignancies, and discuss contribution of EMT to the development of the resistance to Epidermal Growth Factor Receptor (EGFR)-targeted therapies in non-small cell lung cancer (NSCLC). Patients with the tumours bearing specific mutations in EGFR have a good clinical response to selective EGFR inhibitors, but the resistance inevitably develops. Several mechanisms responsible for the resistance include secondary mutations in the EGFR gene, genetic or non-mutational activation of alternative survival pathways, transdifferentiation of NSCLC to the small cell lung cancer histotype, or formation of resistant tumours with mesenchymal characteristics. Mechanistically, application of an EGFR inhibitor does not kill all cancer cells; some cells survive the exposure to a drug, and undergo genetic evolution towards resistance. Here, we present a theory that these quiescent or slow-proliferating drug-tolerant cell populations, or so-called “persisters”, are generated via EMT pathways. We review the EMT-activated mechanisms of cell survival in NSCLC, which include activation of ABC transporters and EMT-associated receptor tyrosine kinase AXL, immune evasion, and epigenetic reprogramming. We propose that therapeutic inhibition of these pathways would eliminate pools of persister cells and prevent or delay cancer recurrence when applied in combination with the agents targeting EGFR.