The development of resistance to anticancer drugs is a major barrier to successful cancer therapy. Tumors that acquire such resistance often employ intricate molecular strategies to evade pharmacological treatment. Among epigenetic RNA modifications, N6-methyladenosine (m6A) is the most prevalent and reversible. Dysregulation of RNA methyltransferases (“writers”), demethylases (“erasers”), and m6A-binding proteins (“readers”) has been observed in various malignancies, influencing oncoprotein levels and promoting tumor initiation, growth, progression, and metastasis. This review highlights the contribution of m6A modifications to therapy resistance. Changes in m6A patterns can alter drug responses by modulating multidrug efflux transporters, enzymes involved in drug metabolism, and direct drug targets. Additionally, m6A-mediated changes affect resistance through DNA repair pathways, adaptive responses (including apoptosis, autophagy, and oncogenic bypass signaling), cancer stem cell traits, tumor immune microenvironment dynamics, and exosomal non-coding RNAs. Notably, several small molecules that target m6A regulatory proteins have shown promising activity in overcoming drug resistance across different cancer types. Development of additional modulators of m6A-related proteins is anticipated to provide novel therapeutic approaches for tackling clinical drug resistance.