Almost 17% of Western patients affected by non-small cell lung cancer (NSCLC) have an activating epidermal growth factor receptor (EGFR) gene mutation. Del19 and L858R are the most-common ones; they are positive predictive factors for EGFR tyrosine kinase inhibitors (TKIs). Currently, osimertinib, a third-generation TKI, is the standard first-line therapy for advanced NSCLC patients with common EGFR mutations. This drug is also administered as a second-line treatment for those patients with the T790M EGFR mutation and previously treated with first- (erlotinib, gefitinib) or second- (afatinib) generation TKIs. However, despite the high clinical efficacy, the prognosis remains severe due to intrinsic or acquired resistance to EGRF-TKIs. Various mechanisms of resistance have been reported including the activation of other signalling pathways, the development of secondary mutations, the alteration of the downstream pathways, and phenotypic transformation. However, further data are needed to achieve the goal of overcoming resistance to EGFR-TKIs, hence the necessity of discovering novel genetic targets and developing new-generation drugs. This review aimed to deepen the knowledge of intrinsic and acquired molecular mechanisms of resistance to EGFR-TKIs and the development of new therapeutic strategies to overcome TKIs’ resistance.