Inducing cancer cell death has always been a research hotspot in life sciences. With the continuous deepening and diversification of related research, the potential value of metal elements in inducing cell death has been explored. Taking iron as an example, ferroptosis, mainly characterized by increasing iron load and driving the production of large amounts of lipid peroxides and eventually leading to cell death, has recently attracted great interest in the cancer research community. After iron, copper, a trace element, has received extensive attention in cell death, especially in inducing tumor cell death. Copper and its complexes can induce autophagy or apoptosis in tumor cells through a variety of different mechanisms of action (activation of stress pathways, arrest of cell cycle, inhibition of angiogenesis, cuproptosis, and paraptosis), which are promising in cancer therapy and have become new hotspots in cancer treatment research. This article reviews the main mechanisms and potential applications of novel copper and copper compound-induced cell death, focusing on copper compounds and their anticancer applications.