Cancer continues to be a leading threat to human health and life. Resistance to anti-cancer drugs is a major impediment towards efficacious cancer treatment. p53 mutations play an important role in cancer cell resistance to chemotherapeutic drugs. The frequency of p53-based chemoresistance is highly associated with the chemical properties of the anticancer drug, the cellular drug target, the biological function being blocked by the chemotherapeutic agent, the genomic instability and alterations of the tumor, as well as its differentiation state. The p53-based molecular mechanisms of anticancer drug resistance are insufficiently understood. With a clear focus on the role of p53 mutations in anticancer drug resistance, the present article reviews the biological structure and function of p53, its regulatory mechanisms, as well as the molecular mechanisms underlying p53 mutation-dependent chemoresistance and possible modalities to surmount this drug resistance. We specifically discuss the roles of p53 in the development of chemoresistance to classical cytotoxic agents including for example cisplatin, doxorubicin, 5-fluorouracil, temozolomide, and paclitaxel. It is expected that the clinical manifestation of drug resistance can be integrated with data obtained from molecular multi-omics analyses addressing the alterations provoked by p53-driven resistance to discover the altered networks in these drug resistant tumors. Thus, novel drugs targeting mutant p53 or mutant p53-based dysregulated pathways, could be developed that may overcome well-defined mutant p53-mediated chemoresistance. Thus, an in-depth understanding of the p53-driven resistance modalities could facilitate the development of novel targeted antitumor drugs and strategies aimed at enhancing the efficacy of current cancer therapeutics.