We survey the history of carbon taxation, the range of market-based instruments (MBIs) of environmental control, and the state of the double dividend debate, in order to suggest directions for future research into MBIs. Returning MBI revenues as lower distortionary taxes rather than as lump sums raises aggregate welfare, but we favour MBIs which raise little or no revenue, for reasons of political acceptability to interest groups. At the same time, the overall case for any environmental improvement is weaker because of general equilibrium interactions with prior distortionary taxes. Research seems most necessary on quantifying the efficiency benefits of market control of heterogeneous polluters, the benefits of environmental improvement, the tax interaction effect, and the various information costs of an MBI, all on a case-by-case basis for different pollutants and places.