The invention of selective homogeneous catalysts in the last 60 years have led to the large scale manufacture of terephthalic acid, the major component of polyethylene terephthalate (PET). It will be shown how the greenness of these processes has increased first with the invention of the soluble cobalt compounds in acetic acid, then with the invention of the metal/bromide catalysts. It is the increase in the selectivity of these catalysts which are directly responsible for large reductions in the production of green-house gases (CO2, CO, CH3Br) and other rate decreasing and color producing by-products. The reduction in by-products and higher yields has also resulted in simplification of the purification of the terephthalic acid and of the commercial plants. The latest efforts to further enhance this greenness is through the invention of catalysts which can successfully oxidize p-xylene to terephthalic acid in high yield in ‘hot' and supercritical water. The structure of MnBr2 ,is the most successful catalyst in ‘hot' water, has been determined. The structure of these homogeneous catalysts, their relationship to solvent properties, and their catalytic mechanisms which are responsible for the greatly enhanced selectivity are given.