Several metals belong to a group of non-biodegradable inorganic constituents that, at low concentrations, play fundamental roles as essential micronutrients for the growth and development of plants. However, in high concentrations they can have toxic and/or mutagenic effects, which can be counteracted by natural chemical compounds called chelators. Chelators have a diversity of chemical structures; many are organic acids, including carboxylic acids and cyclic phenolic acids. The exogenous application of such compounds is a non-genetic approach, which is proving to be a successful strategy to reduce damage caused by heavy metal toxicity. In this review, we will present the latest literature on the exogenous addition of both carboxylic acids, including the Kreb’s Cycle intermediates citric and malic acid, as well as oxalic acid, lipoic acid, and phenolic acids (gallic and caffeic acid). The use of two non-traditional organic acids, the phytohormones jasmonic and salicylic acids, is also discussed. We place particular emphasis on physiological and molecular responses, and their impact in increasing heavy metal tolerance, especially in crop species.