Chemotherapy remains one of the principal modes of treatment for cancer patients. Despite advances in anticancer agents for multiple cancers, development of resistance to classical chemotherapeutic drugs and targeted drugs continues to be a major challenge. Drug resistance which can be either intrinsic or acquired, leads to treatment failure and tumor progression. Drug resistance occurs because of mechanisms that are associated with individual cancer cells or through mechanisms that relate to the microenvironment within tumors. Multiple molecular determinants of intrinsic and acquired resistance including genetic, epigenetic factors, as well as other factors which act at the genomic or cellular level have been identified. This review provides a conspectus on some of the recent discoveries on mechanisms of anticancer drug resistance and the possible ways to revert resistance and thereby improve cancer therapy