Cancer is a deadly disease associated with abnormal cell growth and invasion to various parts of the body. Many drugs such as cisplatin and carboplatin have been used for the treatment of cancer over the years. However, a lack of selectivity toward cancer cells and associated side effects with current treatment options has fueled continued efforts throughout the world to find better anticancer drugs. Over the past decades, copper‐containing compounds have shown excellent anticancer activity. Cu(II) complexes are well studied and show broad‐spectrum pharmacological activity. The redox activity of copper ions contributes to cytotoxic activity in combination with ligands that possess bioactivity. Binding of copper with various types of bidentate, tridentate, and tetradentate ligands can activate the processes of necrosis, apoptosis, and angiogenesis. Copper induces the formation of reactive oxygen species to cleave DNA. Similarly, light‐assisted excitation of Cu(II) complexes in the red region of the electromagnetic spectrum helps produce different reactive species, thereby inducing anticancer activity through a photodynamic mechanism. In general, in vivo and in vitro studies have demonstrated that the administration of copper ions is effective against various cancer cell lines. Herein we discuss the past ten years of research into copper complexes of terpyridine‐, 2,2’‐bipyridine‐, and 1,10‐phenanthroline‐based ligands as potential anticancer agents. The aspects of chemotherapy by redox‐mediated pathways and photodynamic therapy using light‐assisted excitation are reviewed, with a focus on mechanisms of activity, details of important experimental procedures, as well as drawbacks in the design of copper‐containing drugs.