The recent growth in the chemistry of the oxo-molybdenum enzymes has demonstrated the need for developing systematic methods for naming and abbreviating the novel pterin cofactors that bind to the metal ion via the sulfur atoms of an ene-1,2-dithiolate moiety. Historically, the term "molybdopterin" was coined to designate a special pterin that binds molybdenum and the molybdenum-bound form was termed the "molybdenum cofactor". However, recent studies have demonstrated that this novel pterin also binds tungsten. Furthermore, considerable variation has been found in the pterin entity itself. Taken together, these facts show that molybdenum- and tungsten-containing enzymes possess a family of cofactors rather than a single "molybdenum cofactor". This article proposes a unified methodology for describing these cofactors and their metal-free pterin units in light of recent results from protein crystallography. The various numbering schemes that have been used for this heterocycle are considered, as well as the IUPAC rules which are currently being used for related tricyclic compounds. A unified methodology for uniquely designating and abbreviating each cofactor is proposed. The available chemical and spectroscopic information on the pyranopterin entities that are present in the molybdenum and tungsten enzymes, the precursors to these centers, and synthetic pyranopterins are in part the basis of the systematic names and simplifying abbreviations.