The world economy is in a world of hurt.

Europe is wrestling with a debt crisis. Economic growth in powerhouse China appears to be slowing. And in the United States, political paralysis has left policymakers with few tools to fight a slowdown.

Christine Lagarde, head of the International Monetary Fund, warned this week that the world was entering a "dangerous phase." The leader of the World Bank said he loses confidence daily that the global economy can avoid a new recession.

Financial markets fear the worst. The Dow Jones industrials fell almost 6 percent Wednesday and Thursday before an uneasy calm returned Friday. The carnage hit markets in Europe and Asia, too.

Pick a spot on the globe and you'll find economic trouble. Here's a region-by-region guide to what worries the experts.

EUROPE: BATTLING A DEBT CRISIS AND WATCHING GREECE

European policymakers have failed to convince financial markets that they can resolve a massive debt crisis. Investors fear that Greece and other countries will be unable to pay their debts and default, forcing banks to absorb big losses on government bonds.

Greece, Ireland and Portugal have already required bailouts from the European Union and the IMF. Italy and Spain, which are much bigger economies, might need them, too.

A $149 billion bailout has kept Greece afloat for the past year. It's due for another $148 billion rescue negotiated over the summer. But creditors are balking at delivering the second package. They say Greece has fallen behind on commitments to cut government deficits and make its economy more competitive.

European officials are speaking openly of the possibility of a Greek default. The fears have spooked international markets. A default by Greece or any of the other troubled European countries would send shock waves through the banking system and the global economy.

Investors are terrified they'll endure a repeat of the panic that struck Wall Street in 2008. Then, banks stopped lending to each other because they were worried about each other's solvency.

Losses on European government bonds could start a similar crisis. If global credit markets were to freeze the way they did three years ago, that would slow economies on both sides of the Atlantic.

European governments have opted for austerity measures, cutting spending and raising taxes instead of taking steps to jump-start sputtering economic growth.

THE UNITED STATES: FED ACTS, BUT WHAT NOW?

U.S. markets sank this week even though the Federal Reserve offered a bigger dose of economic stimulus than investors had expected: The Fed plans to reshuffle $400 billion of its investments in hopes of pushing down interest rates on mortgages and other long-term loans.

Lower rates are supposed to coax consumers and businesses into borrowing and spending. The Fed also plans to invest proceeds from maturing U.S. Treasury debt into mortgage bonds in an effort to support the housing market.

But economists say the Fed's effort - dubbed Operation Twist after a similar Fed program conducted during the Chubby Checker dance craze of the early 1960s - probably won't make much difference.

Rates on mortgages and other loans are already the lowest in decades. Frightened Americans would rather cut their debts than borrow, and businesses aren't seeing enough sales to justify hiring and expanding despite rock-bottom borrowing costs.

The Fed's announcement underscored the fear that the American central bank had run out of tools to stimulate the economy.

That leaves fiscal policy - government spending programs and tax cuts - as the only other way to juice growth. But political bickering is preventing Washington from doing much of anything.

CongressionalRepublicans are focused on cutting government deficits, not widening them in the name of helping the economy. They are resisting President Barack Obama's $447 billion plan to generate jobs with payroll-tax cuts and more spending for roads, bridges, schools and other infrastructure projects.

Economist Eswar Prasad of Cornell University says the U.S. government should tolerate higher deficits now to spur economic growth - as long as it delivers a credible plan to bring its budget under control in the future.

"We are seeing the exact opposite," he says. The government is cutting spending now, but has yet to deliver a realistic plan to curb medium- and long-term deficits.

CHINA: HINT OF A SLOWDOWN RATTLES INVESTORS

The powerful Chinese economy is supposed to account for a third of global growth this year. Increasingly, other countries depend on China's insatiable demand for raw materials and machinery to give their own economies a lift. The mining towns of western Australia, for instance, are booming as they fill orders from China for iron, zinc and coal.

So any signs the Chinese economy might be slowing are sure to frazzle investors. And a report this week showing that Chinese manufacturing is contracting sent financial markets into a tailspin.

Perhaps it shouldn't have been a surprise: China's central bank has been raising interest rates to slow growth and bring inflation under control.

Analysts say investors overreacted to one limited report. The world's second-biggest economy may be slowing, they say, but it still boasts enviable rates of growth. The IMF this week lopped just a tenth of a percentage point off its estimate for Chinese economic growth this year, bringing it to a still-sizzling 9.5 percent. Its estimate for the U.S. is just 1.5 percent.

Yet despite China's rising power, experts say its economy is still not big or strong enough to compensate for meltdowns elsewhere: Chinese investment and spending is only one-sixth that of the European Union and United States.

"From a global perspective, China's domestic demand is still way too small to offset the impact of a recession" in Europe and the U.S., Deutsche Bank economist Ma Jun said in a report.

To make up for a 3 percentage point drop in growth in those economies, China would have to grow by 18 percent this year, he says.

"This is mission impossible."