Cancers have the ability to develop resistance to traditional therapies, and the increasing prevalence of these drug resistant cancers necessitates further research and treatment development. This paper outlines the current knowledge of mechanisms that promote or enable drug resistance, such as drug inactivation, drug target alteration, drug efflux, DNA damage repair, cell death inhibition, and the epithelial-mesenchymal transition, as well as how inherent tumor cell heterogeneity plays a role in drug resistance. It also describes the epigenetic modifications that can induce drug resistance and considers how such epigenetic factors may contribute to the development of cancer progenitor cells, which are not killed by conventional cancer therapies. Lastly, this review concludes with a discussion on the best treatment options for existing drug resistant cancers, ways to prevent the formation of drug resistant cancers and cancer progenitor cells, and future directions of study.