Copper is an essential microelement that plays an important role in a wide variety of biological processes. Copper concentration has to be finely regulated, as any imbalance in its homeostasis can induce abnormalities. In particular, excess copper plays an important role in the etiopathogenesis of the genetic disease Wilson’s syndrome, in neurological and neurodegenerative pathologies such as Alzheimer’s and Parkinson’s diseases, in idiopathic pulmonary fibrosis, in diabetes, and in several forms of cancer. Copper chelating agents are among the most promising tools to keep copper concentration at physiological levels. In this review, we focus on the most relevant compounds experimentally and clinically evaluated for their ability to counteract copper homeostasis deregulation. In particular, we provide a general overview of the main disorders characterized by a pathological increase in copper levels, summarizing the principal copper chelating therapies adopted in clinical trials.