In the late summer of 2008, two events in quick succession signalled the end of the New World Order. In August, the US client state of Georgia was crushed in a brief but bloody war after it attacked Russian troops in the contested territory of South Ossetia.

The former Soviet republic was a favourite of Washington's neoconservatives. Its authoritarian president had been lobbying hard for Georgia to join Nato's eastward expansion. In an unblinking inversion of reality, US vice-president Dick Cheney denounced Russia's response as an act of "aggression" that "must not go unanswered". Fresh from unleashing a catastrophic war on Iraq, George Bush declared Russia's "invasion of a sovereign state" to be "unacceptable in the 21st century".

As the fighting ended, Bush warned Russia not to recognise South Ossetia's independence. Russia did exactly that, while US warships were reduced to sailing around the Black Sea. The conflict marked an international turning point. The US's bluff had been called, its military sway undermined by the war on terror, Iraq and Afghanistan. After two decades during which it bestrode the world like a colossus, the years of uncontested US power were over.

Three weeks later, a second, still more far-reaching event threatened the heart of the US-dominated global financial system. On 15 September, the credit crisis finally erupted in the collapse of America's fourth-largest investment bank. The bankruptcy of Lehman Brothers engulfed the western world in its deepest economic crisis since the 1930s.

The first decade of the 21st century shook the international order, turning the received wisdom of the global elites on its head – and 2008 was its watershed. With the end of the cold war, the great political and economic questions had all been settled, we were told. Liberal democracy and free-market capitalism had triumphed. Socialism had been consigned to history. Political controversy would now be confined to culture wars and tax-and-spend trade-offs.

In 1990, George Bush Senior had inaugurated a New World Order, based on uncontested US military supremacy and western economic dominance. This was to be a unipolar world without rivals. Regional powers would bend the knee to the new worldwide imperium. History itself, it was said, had come to an end.

But between the attack on the Twin Towers and the fall of Lehman Brothers, that global order had crumbled. Two factors were crucial. By the end of a decade of continuous warfare, the US had succeeded in exposing the limits, rather than the extent, of its military power. And the neoliberal capitalist model that had reigned supreme for a generation had crashed.

It was the reaction of the US to 9/11 that broke the sense of invincibility of the world's first truly global empire. The Bush administration's wildly miscalculated response turned the atrocities in New York and Washington into the most successful terror attack in history.

Not only did Bush's war fail on its own terms, spawning terrorists across the world, while its campaign of killings, torture and kidnapping discredited Western claims to be guardians of human rights. But the US-British invasions of Afghanistan and Iraq revealed the inability of the global behemoth to impose its will on subject peoples prepared to fight back. That became a strategic defeat for the US and its closest allies.

This passing of the unipolar moment was the first of four decisive changes that transformed the world – in some crucial ways for the better. The second was the fallout from the crash of 2008 and the crisis of the western-dominated capitalist order it unleashed, speeding up relative US decline.

This was a crisis made in America and deepened by the vast cost of its multiple wars. And its most devastating impact was on those economies whose elites had bought most enthusiastically into the neoliberal orthodoxy of deregulated financial markets and unfettered corporate power.

A voracious model of capitalism forced down the throats of the world as the only way to run a modern economy, at a cost of ballooning inequality and environmental degradation, had been discredited – and only rescued from collapse by the greatest state intervention in history. The baleful twins of neoconservatism and neoliberalism had been tried and tested to destruction.

The failure of both accelerated the rise of China, the third epoch-making change of the early 21st century. Not only did the country's dramatic growth take hundreds of millions out of poverty, but its state-driven investment model rode out the west's slump, making a mockery of market orthodoxy and creating a new centre of global power. That increased the freedom of manoeuvre for smaller states.

China's rise widened the space for the tide of progressive change that swept Latin America – the fourth global advance. Across the continent, socialist and social-democratic governments were propelled to power, attacking economic and racial injustice, building regional independence and taking back resources from corporate control. Two decades after we had been assured there could be no alternatives to neoliberal capitalism, Latin Americans were creating them.

These momentous changes came, of course, with huge costs and qualifications. The US will remain the overwhelmingly dominant military power for the foreseeable future; its partial defeats in Iraq and Afghanistan were paid for in death and destruction on a colossal scale; and multipolarity brings its own risks of conflict. The neoliberal model was discredited, but governments tried to refloat it through savage austerity programmes. China's success was bought at a high price in inequality, civil rights and environmental destruction. And Latin America's US-backed elites remained determined to reverse the social gains, as they succeeded in doing by violent coup in Honduras in 2009. Such contradictions also beset the revolutionary upheaval that engulfed the Arab world in 2010-11, sparking another shift of global proportions.

By then, Bush's war on terror had become such an embarrassment that the US government had to change its name to "overseas contingency operations". Iraq was almost universally acknowledged to have been a disaster, Afghanistan a doomed undertaking. But such chastened realism couldn't be further from how these campaigns were regarded in the western mainstream when they were first unleashed.

To return to what was routinely said by British and US politicians and their tame pundits in the aftermath of 9/11 is to be transported into a parallel universe of toxic fantasy. Every effort was made to discredit those who rejected the case for invasion and occupation – and would before long be comprehensively vindicated.

Michael Gove, now a Tory cabinet minister, poured vitriol on the Guardian for publishing a full debate on the attacks, denouncing it as a "Prada-Meinhof gang" of "fifth columnists". Rupert Murdoch's Sun damned those warning against war as "anti-American propagandists of the fascist left". When the Taliban regime was overthrown, Blair issued a triumphant condemnation of those (myself included) who had opposed the invasion of Afghanistan and war on terror. We had, he declared, "proved to be wrong".

A decade later, few could still doubt that it was Blair's government that had "proved to be wrong", with catastrophic consequences. The US and its allies would fail to subdue Afghanistan, critics predicted. The war on terror would itself spread terrorism. Ripping up civil rights would have dire consequences – and an occupation of Iraq would be a blood-drenched disaster.

The war party's "experts", such as the former "viceroy of Bosnia" Paddy Ashdown, derided warnings that invading Afghanistan would lead to a "long-drawn-out guerrilla campaign" as "fanciful". More than 10 years on, armed resistance was stronger than ever and the war had become the longest in American history.

It was a similar story in Iraq – though opposition had by then been given voice by millions on the streets. Those who stood against the invasion were still accused of being "appeasers". US defence secretary Donald Rumsfeld predicted the war would last six days. Most of the Anglo-American media expected resistance to collapse in short order. They were entirely wrong.

A new colonial-style occupation of Iraq would, I wrote in the first week of invasion, "face determined guerrilla resistance long after Saddam Hussein has gone" and the occupiers "be driven out". British troops did indeed face unrelenting attacks until they were forced out in 2009, as did US regular troops until they were withdrawn in 2011.

But it wasn't just on the war on terror that opponents of the New World Order were shown to be right and its cheerleaders to be talking calamitous nonsense. For 30 years, the west's elites insisted that only deregulated markets, privatisation and low taxes on the wealthy could deliver growth and prosperity.

Long before 2008, the "free market" model had been under fierce attack: neoliberalism was handing power to unaccountable banks and corporations, anti-corporate globalisation campaigners argued, fuelling poverty and social injustice and eviscerating democracy – and was both economically and ecologically unsustainable.

In contrast to New Labour politicians who claimed "boom and bust" to be a thing of the past, critics dismissed the idea that the capitalist trade cycle could be abolished as absurd. Deregulation, financialisation and the reckless promotion of debt-fuelled speculation would, in fact, lead to crisis.

The large majority of economists who predicted that the neoliberal model was heading for breakdown were, of course, on the left. So while in Britain the main political parties all backed "light-touch regulation" of finance, its opponents had long argued that City liberalisation threatened the wider economy.

Critics warned that privatising public services would cost more, drive down pay and conditions and fuel corruption. Which is exactly what happened. And in the European Union, where corporate privilege and market orthodoxy were embedded into treaty, the result was ruinous. The combination of liberalised banking with an undemocratic, lopsided and deflationary currency union that critics (on both left and right in this case) had always argued risked breaking apart was a disaster waiting to happen. The crash then provided the trigger.

The case against neoliberal capitalism had been overwhelmingly made on the left, as had opposition to the US-led wars of invasion and occupation. But it was strikingly slow to capitalise on its vindication over the central controversies of the era. Hardly surprising, perhaps, given the loss of confidence that flowed from the left's 20th-century defeats – including in its own social alternatives.

But driving home the lessons of these disasters was essential if they were not to be repeated. Even after Iraq and Afghanistan, the war on terror was pursued in civilian-slaughtering drone attacks from Pakistan to Somalia. The western powers played the decisive role in the overthrow of the Libyan regime – acting in the name of protecting civilians, who then died in their thousands in a Nato-escalated civil war, while conflict-wracked Syria was threatened with intervention and Iran with all-out attack.

And while neoliberalism had been discredited, western governments used the crisis to try to entrench it. Not only were jobs, pay and benefits cut as never before, but privatisation was extended still further. Being right was, of course, never going to be enough. What was needed was political and social pressure strong enough to turn the tables of power.

Revulsion against a discredited elite and its failed social and economic project steadily deepened after 2008. As the burden of the crisis was loaded on to the majority, the spread of protests, strikes and electoral upheavals demonstrated that pressure for real change had only just begun. Rejection of corporate power and greed had become the common sense of the age.

The historian Eric Hobsbawm described the crash of 2008 as a "sort of right-wing equivalent to the fall of the Berlin wall". It was commonly objected that after the implosion of communism and traditional social democracy, the left had no systemic alternative to offer. But no model ever came pre-cooked. All of them, from Soviet power and the Keynesian welfare state to Thatcherite-Reaganite neoliberalism, grew out of ideologically driven improvisation in specific historical circumstances.

The same would be true in the aftermath of the crisis of the neoliberal order, as the need to reconstruct a broken economy on a more democratic, egalitarian and rational basis began to dictate the shape of a sustainable alternative. Both the economic and ecological crisis demanded social ownership, public intervention and a shift of wealth and power. Real life was pushing in the direction of progressive solutions.

The upheavals of the first years of the 21st century opened up the possibility of a new kind of global order, and of genuine social and economic change. As communists learned in 1989, and the champions of capitalism discovered 20 years later, nothing is ever settled.

This is an edited extract from The Revenge of History: the Battle for the 21st Century by Seumas Milne, published by Verso. Buy it for £16 at guardianbookshop.co.uk