Despite the development of targeted therapy, drug resistance remains a primary hindrance to curative treatment of various cancers. Among several novel approaches to overcome drug resistance, modulating N6-methyladenosine (m6A) RNA modification was found to be an important strategy in various types of cancer cells. Considered as one of the most common epigenetic RNA modifications, m6A regulates multiple biological processes including cellular proliferation, metabolism, and metastasis through modulation of RNA splicing, degradation, and translation, leading to anticancer drug resistance. This regulatory network is orchestrated mainly by several m6A regulators, including "writers", "readers", and "erasers". It is encouraging that several small molecules targeting m6A regulators have shown great potential in overcoming drug resistance in different cancer cell types, two of which entacapone and meclofenamate, are currently undergoing evaluation. However, the m6A modification participates in complex biological processes and its functions are context-dependent, which has challenged the clinical application of targeting the m6A modification in cancer therapy. In this review, we discuss the molecular mechanisms underlying the m6A modification in regulating anticancer drug resistance through modulation of drug-target interaction and drug-mediated cell death signaling. Alteration of the m6A modification interferes with drug efficacy through modulation of the expression of multidrug efflux transporters (e.g., ABCG2, ABCC9, ABCC10), drug metabolizing enzymes (e.g., CYP2C8), and drug targets (e.g., p53 R273 H). Furthermore, alterations of the m6A modification may protect cells from drug-mediated cell death by regulating DNA damage repair (e.g., p53, BRCA1, Pol κ, UBE2B, and ERCC1), downstream adaptive response (e.g., critical regulators of apoptosis, autophagy, pro-survival signaling, and oncogenic bypass signaling), cell stemness, and tumor microenvironment (e.g., ITGA6, ITGB3, and PD-1). We particularly highlight recent advances in therapeutic strategies targeting the m6A modification with the aim to surmount chemoresistance. The comprehensive understanding of the role of the m6A modification integrated with combined therapeutic strategies, should facilitate the development of future therapeutic strategies to circumvent or surmount drug resistance, thus enhancing therapeutic efficacy. Copyright © 2020 Elsevier Ltd. All rights reserved.