As I mentioned in a recent post, many FUBAR areas of the economy got that way because of decades (and sometimes centuries) of government interference followed by market response. I call these hybrid failures to stress my non-partisan approach to the problem. Most other analysts take ideologically-colored views. Those from the Left jump at the market failure part of the cycle while those on the Right emphasize the government failure part of it. Pollution and its control is certainly a hybrid failure.
Initially, pollution of any sort is, by definition, a type of market failure called a negative externality. The externality is the costs (cleanup, disease, environmental, etc.) imposed by the pollution on society, or rather on innocent victims within societies. Because polluters do not pay the costs of the pollution but reap the benefits they produce more than the socially optimum amount.
The U.S. government reacted to this market failure by capping or limiting the emission of various types of nasties. Polluters responded by weighing the net costs (costs minus benefits) of compliance and cheating so, ultimately, the effectiveness of the cap-only system was a function of the government's diligence monitoring compliance and prosecuting cheaters. Over time, the government's zeal fluctuated. High levels of enforcement were unsustainable due to budget constraints and regulatory capture. In short, politicians found it in their own interest to spend public monies in other, more salient areas in order to garner votes and in order to attract campaign contributions from polluters.
Cap and trade is a modest improvement over straight caps because it offers polluters a third option: selling some or all of their pollution quotas to other polluters who value them more highly. That should induce polluters with a relatively low cost of pollution reduction to sell permits to polluters with a relatively high cost of pollution reduction. That should spur more compliance and a better use of resources. Of course political decisions still rule the system as the government will decide the size of the cap and the distribution of permits. Polluters will try to get an unfair proportion of permits and also to get the overall cap enlarged. And again politicians will see compliance as a drain on public resources that might be better spent elsewhere (like paying down the national debt ... yeah right!).
A tax, on the other hand, gives the government an incentive to enforce compliance, the payment of the tax. Cheating can and will occur but the IRS will try earnestly to minimize it. The government no longer directly decides how much pollution will be allowed but rather sets the tax rate. The market then determines how much pollution is cost effective at that rate. Roughly speaking, the higher the tax, the lower the tolerable quantity of pollution. Presumably, the government will try to maximize its revenue, so it won't increase the tax to the point of eliminating all pollution and hence all its revenue but at the same time it won't be easily swayed by calls for suboptimally low taxes either.
Finally, it would be technically possible to use such a tax to reduce pollution abroad as well by embedding the tax in tariffs. (That may run afoul of the WTO in which case I say then change WTO rules.) That will keep the playing field level and also dissuade polluters from outsourcing or outright moving to other countries to avoid the tax. Cheap imports from China won't look so cheap anymore.
As I noted in One Nation Under Debt, it would behoove us to find a politically tolerable tax to replace the tariffs that paid off the first national debt. A tax on pollution of various sorts might well fit the bill. Most people agree less carbon, mercury, PCBs, etc. would be a good thing. More taxes is a bad thing but if a pollution tax were tied to reductions in income taxes, even if they were less than 1 to 1 reductions, it could work politically, esp. if pushed by some popular, silver-tongued leader.