It has been 26 years since Soviet leader Mikhail Gorbachev stood before the United Nations General Assembly and used Woodrow Wilson's phrase "new world order" to describe the "profound social change" that was about to take place in the relations between the world's nations and their people. The world, he said, was about to experience a major change driven by "new nations and states, new public movements and ideologies."

Over the next quarter-century, Mr. Gorbachev's new world order became, simply, the world order: a world built on a broad agreement among most major countries that democracy and liberal economy were desirable goals; a world with only one superpower; a world where international institutions could govern trade, monetary and financial affairs and military conflicts; a world in which poorer countries gradually adopted the values and institutions first popularized in the West; and a world dominated by the United States, its military and its dollar.

As the UN once again convenes its General Assembly this week – and surprising words emerge from the speeches of Iranian, Chinese, Russian and American leaders – there is a profound sense, among many observers, that the world is once again reordering itself. The old certainties have collapsed or faded, and new threats challenge them.

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The United States no longer always calls the shots, and when it tries to, as in the Middle East, it sometimes fails badly. It may no longer be the only superpower, as China expands to become one and uses its military to torment Japan and to bid for control over the South China Sea. Rival models of nationhood, far more economically and politically authoritarian, are increasingly influential, if not united.

The failures of Iraq and Afghanistan and the tumult of the post-2008 economic crisis have left many countries searching for other influences. An authoritarian, territorial and anti-Western Russia has brought back some of the harsh logic of the Cold War. And a group of defiantly anti-democratic states and violent non-state movements are exercising their own influence – most notably in the failed states created by Iraq's aftermath, where the Islamic State's well-financed bid for a brutal theocracy is provoking a new, very different sort of international war, one whose bizarre coalitions we saw emerging in New York this week.

Old-style nationalism, from China to Scotland, has become a force once again. And international institutions have failed to solve some of the world's most damning problems, notably carbon-driven atmospheric change.

In a recent lecture, Michael Ignatieff, now at Harvard University, spoke of the failure of the old institutions and powers to hold together "the tectonic plates of a world order that are being pushed apart by the volcanic upward pressure of violence and hatred." The old rules don't seem to apply any more. People who make a living observing the interactions between nations almost all say that some form of an even newer world order is taking shape around us – but there is little agreement as to what it looks like.

Here are five major, competing visions of the emerging international order, and the thinkers who argue on behalf of each. If history is a guide, the world of the next decade will not resemble any one of them purely, but will be influenced by many of them. In 1988, Mr. Gorbachev's "new world order" seemed to be a fringe prognostication, dismissed by many. What we are witnessing today may be an equally unpredictable shift.

The world becomes rudderless

The United States is declining in power and influence. That may not be true in any way you could measure or prove, but it is what much of the world believes today – and when it comes to power and influence, perceptions are often as important as reality.

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At the same time, many believe that no other country, or bloc of countries, is really interested in becoming the world's cop, banker, supermarket, sugar daddy or scold. Europe is struggling to maintain its own unity and restore its economy, Japan is looking inward, China is mainly interested in China's interests, and blocs of new powers such as the so-called BRICS countries (Brazil, Russia, India, China and South Africa) have failed to act in any co-ordinated way. As a result, this argument goes, the world is increasingly fragmented, without a single vision (or a single big bully) to shape its direction. Those who buy this see it as either a good thing or a bad thing.

On the "bad thing" side of the equation are U.S. scholars Ian Bremmer and Nouriel Roubini, who argued in an influential 2011 essay, and in a book by Mr. Bremmer, that "we are now living in a G-Zero world [as opposed to a well-organized G-20 or G-8 world], one in which no single country or bloc of countries has the political and economic leverage – or the will – to drive a truly international agenda." On crucial issues such as climate change, international trade, facing up to Russian or Islamist threats, or controlling nuclear arms, it has become nearly impossible to reach international consensus, and the result, they say, "will be intensified conflict on the international stage over vitally important issues."

A less pessimistic version of this rudderless-world is proposed by Stewart Patrick of the Council on Foreign Relations. He sees an "unruled world," but one of ever-changing coalitions and improvisations, rather than the dark nihilism of the G-Zero vision.

"I see even more ad hoc actions taking place, with more fluid coalitions to deal with global problems and selective use of frameworks – there's going to be a lot more compartmentalizing of issues," he says.

But none of it will be permanent: There will be neither guaranteed Western influence over events, nor an organized anti-Western bloc of nations taking shape as there was during the Cold War (because their mutual rivalries and disagreements tend to trump any solidarity).

Mr. Patrick points to Barack Obama's UN speech this week, in which he called for world order – but in the form of ad hoc coalitions, among countries that might otherwise be enemies, to deal with the threats of Russia and the Islamic State. Other issues, such as the climate threat and Internet governance, may not be dealt with at all. "There's very little appetite to remake things," he says, but at the same time the old institutions won't have the same drivers at the wheel – or, sometimes, any driver at all.

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A new Cold War erupts

What if this new world isn't fragmented by chaos and disharmony, but instead is divided in two by conflict and enmity? A number of influential thinkers believe that the signature event of our age is not the messy ad hoc coalition of the Middle East but rather Russian President Vladimir Putin's seizure of Crimea and military meddlings in eastern Ukraine and northern Georgia. In this vision, the new world order is being replaced with something a lot like what came before it – a showdown between ideological blocs allied against one another.

In the view of this school of thinkers, Mr. Putin's Crimean adventures are not simply a regional problem to be dealt with through tough sanctions and military postures, but one event in a longer showdown between either Russia and its allies – often called the "revisionist states," for their desire to turn back the clock to pre-1989 days – and the West.

"China, Iran, and Russia never bought into the geopolitical settlement that followed the Cold War, and they are making increasingly forceful attempts to overturn it," Walter Russell Mead, a leading New Cold War theorist, argued this summer. "That process will not be peaceful, and whether or not the revisionists succeed, their efforts have already shaken the balance of power and changed the dynamics of international politics."

Critics of this view point out that Mr. Putin's embrace of ethnic nationalism and the military meddling do not appear to be part of some imperial bid to dominate the world, but rather to make the most of decline and weakness – and that there is nothing you'd call a proper alliance between Russia, China (which Moscow often sees as an enemy) and Iran and Syria (given that Russia often sees Islamic states and its own large Muslim population as a principal threat).

But the Russian-provoked violence in Ukraine, including the downing of Malaysia Airlines Flight 17, has certainly changed the way people look at international affairs: Russia has not just been kicked out of the G8, but out of the old world of interational co-operation. Edward Lucas, a writer with The Economist who warned of a "new cold war" with Russia in a 2008 book of that title, argues that this can be seen only as part of a major new East-West showdown.

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"Russia is a revisionist power. It has the means to pursue its objectives. It is winning; and greater dangers lie ahead," Mr. Lucas said in testimony to the British parliament this month. "Our weakness over Ukraine (and before that, Georgia) has set the stage for another, probably more serious challenge to European security. … Estonia, Latvia and Lithuania are loyal American allies and NATO members. These are our frontline states: The future of the world we have taken for granted since 1991 hangs on their fate."

A Chinese superpower takes hold

On the other hand, some believe that the end of superpower dominance is really a transition. What if Beijing overtakes Washington not just economically, but militarily and politically as well? A number of people believe this is the major emerging trend.

"The question of whether China is becoming a status quo power, a contented power, a country that's basically willing to live within the confines of the existing system – it seems to me increasingly that that is not the case," says Aaron Friedberg, a national-security official in the George W. Bush White House and now a political scientist at Princeton University's Woodrow Wilson School. "When you look at what Beijing is doing, for example, with the maritime disputes with their neighbours, they're trying to change the status quo in some pretty significant ways."

The main critique of this vision is that China does not appear to desire to be a global superpower, in the conventional Cold War sense: Its interests are largely mercantile; its only territorial ambitions seem to involve securing its borders; and it does not seek to impose its ideology or culture on the countries with which it engages – even those in Africa where it has a colonial-like economic role. China depends almost entirely on its economic relations with the wider world and would not dare to jeopardize them.

But a number of influential thinkers – as well as senior Pentagon officials – believe this is changing, especially under Xi Jinping, who since becoming president in 2012 has increasingly brought the military's voice into Beijing's discourse. This has led many to argue that China is looking to challenge the United States – certainly within the South China Sea region and the eastern hemisphere, and maybe even more widely. It has become increasingly self-confident and independent – and, because it has eliminated severe poverty and raised living standards within its borders, it is not quite as dependent on outside trade as it once was.

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This has led a number of scholars, most on the right, to argue that Western countries should prepare a policy of containment for China, much like that imposed on the Soviet Union during the Cold War. "In his final years in office," military scholar John Hemmings wrote in an essay this summer, "Obama must decide with regional allies and partners what the red line is for China. And then he must act, if that line is crossed."

His rhetoric echoes that of Robert Kaplan, the apocalyptic-minded U.S. political scientist, who argued in 2005 that "the American military contest with China in the Pacific will define the 21st century." That hasn't come true yet, but there are an alarming number of people, in both the U.S. and the Chinese military, who believe that it will and who are actively preparing for such a conflict – and military timetables have an alarming habit of being put to use.

More hawkish voices argue that Beijing is preparing for superpower status in other ways. "Do they intend to conquer the Philippines? No. But would they like to exercise a dominant influence across their entire region, I'd say yes," says Mr. Friedberg, whose most recent book is A Contest for Supremacy: China, America and the Struggle for Mastery in Asia. "They've never liked or accepted American alliances, and they're increasingly dissatisfied with those. They're trying to use economic leverage to strategic ends as well."

We fight over climate and scarce resources

What if no specific superpower or alliance becomes a major enemy, but the Earth itself does? As petroleum becomes more scarce and valuable, will we have global wars and conflicts over access to it? Will the devastating effects of climate change create new rifts in the global order?

This is not a new model. The idea of dwindling resources or an unstable climate becoming the main sources of global conflict has been around for almost 25 years; just such a resource-and-climate showdown has been predicted by observers such as Mr. Kaplan (in his 1994 essay, The Coming Anarchy) and Canada's Thomas Homer-Dixon (in such 1990s works as Environmental Scarcity and Global Security and Environment, Scarcity and Violence).

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It also has become a theme for environmental historians and activists such as Jared Diamond and Bill McKibben, who argue that climate and resources will soon trump all other politics.

Surprisingly, this has not yet happened. While petroleum rights have played a role in a few conflicts such as the 2011 NATO-supported overthrow of Libya's Moammar Gadhafi, in general, conflicts during the past quarter-century have not been "about oil" – most of the big ones have been about the old motives of territory, religion and ethnicity (although many have been financed with petroleum revenues). And the notion of climate-driven conflict, beyond a few marginal examples, remains largely a hypothesis.

But there is a distinctly new dynamic to the politics of energy and climate, one that could, some believe, create a difficult relationship between the major powers and their people.

"Resources aren't becoming scarce as much as they're becoming increasingly problematic – those that were easy to obtain are depleted, and those that are left are difficult, in many respects," says Michael Klare, the U.S.-based author of such works as Resource Wars and The Race for What's Left: The Global Scramble for the World's Last Resources.

"Either they're in contested areas like the South China Sea or the Arctic, or you're relying more on natural gas, which gives Russia and Iran a lot more clout … or they're causing a domestic struggle over practices such as hydro-fracking."

This, he notes, leads to a paradoxical problem: Increasingly, countries see these hard-fought resources as necessary tools for their own independence (a petro-centric belief that afflicts everyone from Vladimir Putin to Canada's Conservatives to Greenland's independence-minded Inuit to the militants in the Islamic State). By relying on this tool – at the same time as countries such as Germany walk away from non-polluting technologies such as nuclear power – they are further evading any confrontation with a looming climate crisis.

While the result may not play out like the global apocalypse some members of this group foresee, it is increasingly likely that both energy resources and climate change are going to be major components in the emerging world order.

The world muddles through as it has before

Any of the preceding visions could become the one that people in the 22nd century use to describe our era: as one of chaos, as one of division, as one of a new superpower conflict, or as one of resource panic. But it is just as likely, given recent history, that all four will provide at least some sources of tension in a world order that is not so much new as slightly different – one where the same old creaky institutions, and a new set of compromises, allow the world to muddle through.

What if conflicts don't drive nations apart, but bring them together? This is not as farfetched as it sounds, a number of scholars say.

That case is made most assertively by political scientist John Ikenberry of Princeton University, who notes that, despite limited-scale regional conflicts, the liberal order established after the Second World War remains robust and unchallenged. Russia and China, he writes, "are not full-scale revisionist powers but part-time spoilers at best." Both countries are deeply integrated into the liberal institutions of the world: "They are geopolitical insiders, sitting at all the high tables of global governance." And, he notes, most of the values and principles that 50 years ago were considered "Western" are now truly universal, practised and embraced even by those countries that most aggressively oppose the United States. He feels that the best response from Western countries is not to engage in conflict but to deepen engagement – economic and institutional – between countries.

Daniel Drezner of Tufts University, in a book this year titled The System Worked, noted that the period after the 2008 economic crisis was one of surprising international co-operation: Not only did the major powers (including China and the United States) make important compromises and agreements to avoid global ruin, but the postwar international organizations – the UN, the World Bank, the International Monetary Fund, the G20 – suddenly started functioning well as problem-solving bodies. Problems such as piracy, offshore banking, currency imbalance and lax banking regulations have been resolved in recent years through deep international co-operation – some of it involving countries, such as China and Iran and Russia, that are opposed to one another in other spheres. Tensions and conflicts exist, but they have not led to isolation; the world is not divided in two.

These thinkers could be equally wrong – their views sound like those which were popular on the eve of the First World War. But they provide a reminder that awkward, yet ultimately successful compromise and stumbling, rather than global cataclysm, have been the norm for seven decades, and may still be the cornerstone of the newest world order.