Inorganic anions inhibit the metalloenzyme carbonic anhydrase (CA, EC 4.2.1.1) generally by coordinating to the active site metal ion. Cyanate was reported as a non-coordinating CA inhibitor but those erroneous results were subsequently corrected by another group. We review the anion CA inhibitors (CAIs) in the more general context of drug design studies and the discovery of a large number of inhibitor classes and inhibition mechanisms, including zinc binders (sulphonamides and isosteres, dithiocabamates and isosteres, thiols, selenols, benzoxaboroles, ninhydrins, etc.); inhibitors anchoring to the zinc-coordinated water molecule (phenols, polyamines, sulfocoumarins, thioxocoumarins, catechols); CAIs occluding the entrance to the active site (coumarins and derivatives, lacosamide), as well as compounds that bind outside the active site. All these new chemotypes integrated with a general procedure for obtaining isoform-selective compounds (the tail approach) has resulted, through the guidance of rigorous X-ray crystallography experiments, in the development of highly selective CAIs for all human CA isoforms with many pharmacological applications.