Female breast cancer is the world’s most prevalent cancer in 2020. Chemotherapy still remains a backbone in breast cancer therapy and is crucial in advanced and metastatic breast cancer treatment. The clinical efficiency of chemotherapy regimens is limited due to tumor heterogeneity, chemoresistance, and side effects. Chemotherapeutic drug combinations with natural products hold great promise for enhancing their anticancer efficacy. Curcumin is an ideal chemopreventive and chemotherapy agent owning to its multitargeting function on various regulatory molecules, key signaling pathways, and pharmacological safety. This review aimed to elucidate the potential role of curcumin in enhancing the efficacy of doxorubicin, paclitaxel, 5-fluorouracil, and cisplatin via combinational therapy. Additionally, the molecular mechanisms underlying the chemosensitizing activity of these combinations have been addressed. Overall, based on the promising therapeutic potential of curcumin in combination with conventional chemotherapy drugs, curcumin is of considerable value to develop as an adjunct for combination chemotherapy with current drugs to treat breast cancer. Furthermore, this topic may provide the frameworks for the future research direction of curcumin–chemotherapy combination studies and may benefit in the development of a novel therapeutic strategy to maximize the clinical efficacy of anticancer drugs while minimizing their side effects in the future breast cancer treatment.