It is now widely recognized that sulfur dioxide pollution of the atmosphere can no longer be tolerated. Thus, widespread attention has been given to removing sulfur from the fuels that we now burn. Solution of this problem is quite simple for natural gas; at the opposite extreme, for the case of coal, the problem has not yet been solved. This review describes efforts to desulfurize petroleum products, efforts which have been successful to a large extent but which have not achieved the degree of success ultimately required by society. As will be seen, such success presents a catalysis problem which is by no means simple and on which only evolutionary developments have been made to date. Here, then, is an excellent opportunity to exploit years of effort on catalytic theory in a way which will benefit mankind.