Numerous physiological processes happening in the human body, including cerebral development and function, require the participation of biometal ions such as iron, copper, and zinc. Their dyshomeostasis may, however, contribute to the onset of Alzheimer's disease (AD) and potentially other neurodegenerative diseases. Chelation of biometal ions is therefore a therapeutic strategy against AD. This review provides a survey of natural and synthetic chelating agents that are or could potentially be used to target the metal hypothesis of AD. Since metal dyshomeostasis is not the only pathological aspect of AD, and the nature of this disorder is very complex and multifactiorial, the most efficient therapeutics should target as many neurotoxic factors as possible. Various coumarin derivatives match this description and apart from being able to chelate metal ions, they exhibit the capacity to inhibit cholinesterases (ChEs) and monoamine oxidase B (MAO-B) while also possessing antioxidant, anti-inflammatory, and numerous other beneficial effects. Compounds based on the coumarin scaffold therefore represent a desirable class of anti-AD therapeutics.