Copper is an essential micronutrient that is a cofactor for various enzymes involved in multiple cellular processes. Melanoma patients have high serum copper levels, and elevated copper concentrations are found in melanoma tumors. Copper influences the activity of several melanoma-related proteins involved in cell survival, proliferation, pigmentation, angiogenesis, and metastasis. Targeting these processes with copper chelators has shown efficacy in reducing tumor growth and overcoming drug resistance. In contrast, excessive copper can also have detrimental effects when imported into melanoma cells. Multiple distinct cellular effects of copper overload, including the induction of different types of cell death, have been reported. Cuproptosis, a novel type of copper-dependent cell death, has been recently described and is associated with the metabolic phenotype. Melanoma cells can switch between glycolysis and oxidative phosphorylation, which are crucial for tumor growth and drug resistance. In this respect, metabolic plasticity might be exploited for the use of copper-delivery strategies, including repurposing of disulfiram, which is approved for the treatment of noncancer patients. In addition, the development of nanomedicines can improve the targeted delivery of copper to melanoma cells and enable the use of these drugs alone or in combination as copper has been shown to complement targeted therapy and immunotherapy in melanoma cells. However, further research is needed to explore the specific mechanisms of both copper restriction and excess copper-induced processes and determine effective biomarkers for predicting treatment sensitivity in melanoma patients. In this review, we discuss the dual role of copper in melanoma biology.