Persister cells constitute a subset of cancer cells that exhibit resistance to anticancer therapies. They evade anticancer drug-induced cell death by slowing down the cell cycle and transiently adapting to the drugs through multiple pathways. Subsequently, these persister cells function as reservoirs, leading cancer cells towards diverse and irreversible mechanisms of drug resistance. The causes of treatment resistance in persister cells have been reported to be primarily epigenetic changes, rather than irreversible genetic mutations. Acquisition of stem-like features, epithelial-to-mesenchymal transition, alterations in survival and apoptosis signaling, changes in metabolism, variations in the tumor microenvironment, and acquisition of immune escape mechanisms are reported to be involved in the survival of persister cells. Although various therapeutic interventions have been explored for each of these aspects, few have been clinically applied. In this article, we place a particular emphasis on EGFR lung cancer and persister cells. We discuss the reasons why EGFR tyrosine kinase inhibitors fail to achieve curative outcomes and consider the biological characteristics of persister cells. We also review an overview of potential therapeutic strategies to overcome persister cell-induced resistance.