Cancer drug resistance represents the main obstacle in cancer treatment. Drug-resistant cancers exhibit complex molecular mechanisms to hit back therapy under pharmacological pressure. As a reversible epigenetic modification, N6-methyladenosine (m6A) RNA modification was regarded to be the most common epigenetic RNA modification. RNA methyltransferases (writers), demethylases (erasers), and m6A-binding proteins (readers) are frequently disordered in several tumors, thus regulating the expression of oncoproteins, enhancing tumorigenesis, cancer proliferation, development, and metastasis. The review elucidated the underlying role of m6A in therapy resistance. Alteration of the m6A modification affected drug efficacy by restructuring multidrug efflux transporters, drug-metabolizing enzymes, and anticancer drug targets. Furthermore, the variation resulted in resistance by regulating DNA damage repair, downstream adaptive response (apoptosis, autophagy, and oncogenic bypass signaling), cell stemness, tumor immune microenvironment, and exosomal non-coding RNA. It is highlighted that several small molecules targeting m6A regulators have shown significant potential for overcoming drug resistance in different cancer categories. Further inhibitors and activators of RNA m6A-modified proteins are expected to provide novel anticancer drugs, delivering the therapeutic potential for addressing the challenge of resistance in clinical resistance.