We all know that libertarians believe in drug legalization, the free market, free speech and freedom of religion.
But what everyone forgets is that libertarianism effectively prohibits pollution of any kind (air, water, noise, etc.). It doesn't just tax it or discourage it. It makes it virtually impossible.
Philosophers from Thomas Paine and William Godwin to Robert Nozick and Frederick Hayek have written much about libertarianism. But I'm going to quote Ayn Rand, as she is the modern face of libertarianism (and the woman for which Ron Paul named his son):
"The basic right of man is to live his life without being harmed by others. This implies the requirement to refrain from harming others as well, since all men share this most fundamental right."
However, modern Objectivists rarely point out that burning coal or pouring chemicals into a river causes harm to others in the same way that taxation does. And like taxation, pollution uses force to cause harm. According to the World Health Organization, air pollution from burning coal kills more than 1 million people every year, and causes physical harm and monetary harm (aka "theft") to many many more. In Rand's philosophy, pollution is the moral equivalent of robbery or rape.
So, what is the role of government when one individual (the owner of a coal plant) is causing harm to others against their will?
Modern "right-wing" politicians (aka "the Republican party") advocate that we should ignore these harms. The coal plant is providing electricity and creating jobs, and one could argue that this benefit outweighs the harm (to the society as a whole, if not to each individual). Despite what Paul Ryan and the Koch Brothers would like you to believe, this is not "free market capitalism". This is tyranny. This is what Ayn Rand calls "collectivism" -- the government using force to decide that the "needs" of the entire society are more important that the rights of any one individual.
Modern "left-wing" politicians (aka "the Democratic party") advocate that we should "regulate" these harms. This means using government force to reduce "excessive" pollution, and to tax the rest. If the scientists at the EPA decide that burning coal causes $100 worth of damage to every American, then left-wing politicians will levy a tax on coal burning equal to $100 per American. They could then turn around and give this money to each person that was harmed. However, more often, that money is used to pay for government programs that attempt to ameliorate that harm (e.g. health care) or reduce future harm (e.g. investment in "alternative" energy).
As with the Republican solution, the Democrat's solution is also "collectivism". It is the government using force to put the collective good ahead of individual rights.
Libertarianism holds that both the Republicans and Democrats are allowing (and even encouraging) a moral wrong. No one has a right to harm any other person without using the free market to reach an agreement beforehand. I can't just burn down your house because I feel like it, and then pay you $100 the next day because I feel that this is the "fair value" of your home. If you want to sell me your house, you are free to do so. But we must come to an agreement *before* I burn down your house.
In the case of pollution, this means that every single person harmed by pollution must agree to it beforehand. As one individual, I could decide that I'm willing to let a coal plant pollute my air if they pay me $100 each year. Every single person could reach this same agreement with the coal company. This is the free market at work: individuals determining how much something (such as clean air) is worth *before* they sell it.
It's even possible that everyone would come together and legally delegate a representative to negotiate on their behalf. This is what unions do, and it allows the workers to continue to do their jobs and live their lives while a fair market price is determined.
However, unions are voluntary organizations. If you don't want to work for GM, you don't have to. But breathing isn't voluntary. If you pollute my air, you are using force to harm me, and it is the legitimate role of any libertarian government to stop that harm (by using the courts and police force to physically prevent this harm from taking place).
As it is virtually impossible that 7 billion humans will all agree to have their air polluted, libertarianism and pollution are incompatible in the real world (unless the polluter finds a way to contain the pollution in a bubble built on private land, or to stop the pollution at the source -- but then it isn't really "pollution", is it?)
At this point, libertarians might choose to compromise their principles in exchange for efficiency. For example, I would like to be able to drive a gasoline-powered vehicle so that I can visit my family on Thanksgiving. Therefore, I elect a government that enforces my "right" to pollute, even though I am violating the rights of others. This is democracy. But it isn't libertarianism.