The corporation is the second-largest privately owned business in America, and as a result, the family is the third wealthiest in the world.

The brothers didn't just make money - they spent it, more than $100 million on Republican and libertarian causes. Their extensive donations, which spanned decades, dramatically reshaped American politics in the late 20th century. But it was only in the past 10 years that their name became an epithet on the left. So what changed?

It was not that Americans suddenly became afraid of money and politics mixing. That had been a centuries-long obsession, one that grew particularly sharp in the late 19th century when the US became the world's leading manufacturer and millionaires, then billionaires, proliferated. The super-wealthy openly bought access to the government, sparking a backlash that resulted in a raft of progressive reforms and a new income tax for the wealthiest households.

Nor was it that the Kochs were new to the world of buying influence. The family patriarch, Fred Koch, made his millions in the oil industry in the 1920s and '30s. He put that new wealth to political use, helping to found the John Birch Society in 1958. The Birch Society, a semi-secret and increasingly paranoid right-wing organisation, dedicated itself primarily to fighting communism, though the group also found time to oppose black civil rights and fluoridation (which it believed was part of a plot to turn the US into a communist country).

The Koch brothers followed in their father's footsteps, especially David, who in 1980 was the vice-presidential candidate for the Libertarian Party. Disappointed that the ticket drew only 1.1 per cent of the vote, David turned his attention, and his bank account, to building a libertarian infrastructure in the US. They were already pursuing traditional strategies, such as funding the Cato Institute, a libertarian think tank. But after 1980 they looked for more aggressive ways to change politics without winning elections, such as funding the American Legislative Exchange Council, which writes model legislation for state governments in order to enact a national conservative agenda while bypassing the federal government.

The Koch brothers wanted to cut taxes, shrink the government and deregulate everything. It was essentially the Republican agenda, shorn of any social conservatism (the Kochs supported abortion access, gay rights and open immigration, even though they often funded groups and candidates opposed to those policies).

Yet while some activists noticed the Koch brothers' political spending, it was not until 2010 that the Koch name became a bogeyman. There was no single precipitating incident. The global financial crisis temporarily convinced Americans that more regulation was a good thing, and that perhaps billionaires should not be in charge of the world economy. Even conservatives were insisting that federal programs such as Medicare and social security be protected.

But that wasn't the only force propelling the Kochs into the spotlight. The rise of the Tea Party, a purportedly grassroots movement with a strong libertarian edge, brought more attention to the well-funded libertarian movement and its architects. Though the Kochs denied any formal ties to the Tea Party, the groups that they founded, especially Americans for Prosperity, played a crucial role in the 2010 Republican landslide that brought the Tea Party to greater prominence.

Nothing, though, was more significant than the Supreme Court's decision in a campaign finance case in 2010. In Citizens United v FEC, the court held that corporations had free-speech rights and that money was a form of speech. As a result, the court determined it was unconstitutional for the federal government to restrict political donations from corporations. This decision and others led to a sharp increase in "dark money", vast political donations made with no disclosure of who was making them.

It's hard to overstate just how divisive this decision was. Following Citizens United, public opinion of the Supreme Court plunged and has never recovered.

What ultimately made the Kochs the avatar of dark money in the US was an August 2010 article in the New Yorker by investigative reporter Jane Mayer. By centring her story about the rise of anonymous, unlimited spending in politics, she gave a face to a faceless problem. From then on, the Kochs became synonymous, at least on the left, with the problem of untraceable political contributions.

Ever since, the Kochs have been bogeymen of the left. And while that reputation was not entirely undeserved - their massive wealth really did reshape American politics - David Koch's death is a reminder that his family represents a much broader problem fuelling distrust in American politics.

Perhaps in time the Koch influence will wane. But the broader issue of anonymous funding will plague American politics for decades, unless a future Supreme Court returns the right of free speech - and political power - to people, not corporations.