RNA methylations play critical roles in RNA processes, including RNA splicing, nuclear export, nonsense-mediated RNA decay, and translation. Regulators of RNA methylations have been shown to be differentially expressed between tumor tissues/cancer cells and adjacent tissues/normal cells. N6-methyladenosine (m6A) is the most prevalent internal modification of RNAs in eukaryotes. m6A regulators include m6A writers, m6A demethylases, and m6A binding proteins. Since m6A regulators play important roles in regulating the expression of oncogenes and tumor suppressor genes, targeting m6A regulators can be a strategy for developing anticancer drugs. Anticancer drugs targeting m6A regulators are in clinical trials. m6A regulator-targeting drugs could enhance the anticancer effects of current chemotherapy drugs. This review summarizes the roles of m6A regulators in cancer initiation and progression, autophagy, and anticancer drug resistance. The review also discusses the relationship between autophagy and anticancer drug resistance, the effect of high levels of m6A on autophagy and the potential values of m6A regulators as diagnostic markers and anticancer therapeutic targets.