Copper is a transition metal and an essential element for the organism, as alterations in its homeostasis leading to metal accumulation or deficiency have pathological effects in several organs, including the central nervous system. Central copper dysregulations have been evidenced in two genetic disorders characterized by mutations in the copper-ATPases ATP7A and ATP7B, Menkes disease and Wilson’s disease, respectively, and also in multifactorial neurological disorders such as Alzheimer’s disease, Parkinson’s disease, amyotrophic lateral sclerosis, and multiple sclerosis. This review summarizes current knowledge about the role of copper in central nervous system physiology and pathology, reports about unbalances in copper levels and/or distribution under disease, describes relevant animal models for human disorders where copper metabolism genes are dysregulated, and discusses relevant therapeutic approaches modulating copper availability. Overall, alterations in copper metabolism may contribute to the etiology of central nervous system disorders and represent relevant therapeutic targets to restore tissue homeostasis.