The epidermal growth factor receptor (EGFR) is among the research subjects of most interest and remains genuinely attractive due to its key role in regulating the main conserved signaling pathways responsible for cell growth, survival, and proliferation. Dysregulation of the signaling pathways leads to cell malignant transformation, tumor progression, and metastasis. Therefore, EGFR is considered as one of the main targets for anticancer drug development. Although several generations of novel anti-EGFR drugs have been successfully developed, acquisition of drug resistance and the mutation status of the downstream effector protein KRAS significantly reduce the tumor response to therapy. The review focuses on the current approaches to anti-EGFR therapy. Drugs designed to block the EGFR-mediated signaling are described, including monoclonal antibodies, tyrosine kinase inhibitors, and immunotoxins. Mechanisms of acquired resistance to anti-EGFR therapy are discussed, and combination treatment strategies are proposed to improve the efficacy of the available drugs. Finally, promising antitumor agents, including ribonucleases (RNases) of various origins, are considered.