Obama's re-election averts the immediate prospect of the United States designating China a currency manipulator, which Romney had promised to do on his first day in office. That would have been a setback to relations and could even have triggered a trade war between the world's two biggest economies.
During his first term, Obama stepped up trade complaints against China but also sought to deepen ties with Beijing to diminish the prospects of a confrontation with a Chinese military that is starting to challenge U.S. pre-eminence in the Asia-Pacific.
This week, China embarks on its own once-in-a-decade leadership transition that will be critical in setting the tone for relations between the powers in the years ahead.
The run-up to the Communist Party Congress, which opened Thursday, has seen an escalation in tensions between China and Japan over disputed islands in the East China Sea. The U.S. has a treaty obligation to help Japan if it is attacked — a scenario Washington is eager to avoid.
Obama will be looking to reassure China that the U.S. does not seek to block its rise as a global power but will also be pressing it to abide by international norms. A strident nationalistic tone in China's state rhetoric in its dispute with Japan has fueled concerns that China's new leaders could increasingly resort to such patriotic appeals if the nation's juggernaut economy slows and public dissatisfaction with the Communist Party grows further. That heightens the risk of a more adversarial relationship between the U.S. and China.
During his first term, Obama made improving relations with Russia a priority. His so-called reset policy yielded dividends, including a major nuclear arms control pact, Russia's entry into the World Trade Organization and Russian help with the U.S. war in Afghanistan.
But as he moves into his second term, Obama's Russia policy could take a bumpy turn. Among the areas of contention: Russia's backing of Assad's regime in Syria and opposition to increased Western sanctions on Iran.
In March, Obama was caught on a microphone telling then-President Dmitry Medvedev that the U.S. would have more flexibility to work on missile defense issues after the election. Moscow wants Obama to scale back the U.S. missile defense plans in Eastern Europe that Russia has stridently opposed. But any move by the White House to limit those plans would provoke cries of appeasement from Republicans, who will continue to control the House of Representatives.
Obama is pushing to lift Cold-War era trade restrictions that are preventing U.S. companies from enjoying the full benefits of Russia's entry into the WTO. U.S. lawmakers, including many from Obama's party, are tying the removal of restrictions to another bill that would target senior Russian officials implicated in human rights abuses with financial sanctions. The Kremlin has said it would retaliate with economic measures of its own.
There's little appetite in Washington to haggle with North Korea for possible deals to provide aid in return for a rollback in Pyongyang's nuclear program.
Last year, Obama's sole attempt at negotiating a nuclear freeze with North Korea in exchange for food aid ended in failure when Pyongyang launched a long-range rocket in defiance of U.N. ban. Now, North Korea is hinting that it may withdraw from its 2005 commitments on denuclearization as a prelude to declaring itself a nuclear power, which would bring strong U.S. objections.
Washington could respond by moving to tighten already tough sanctions against the North, but that could likely leave the U.S. at odds with the winner of a December presidential election in key ally South Korea. The next president is expected to adopt a more conciliatory stance toward the North than the incumbent, Lee Myung-bak, who has been Obama's staunchest backer in Asia.
The U.S. will continue urging China to use its fraternal relations and economic leverage over North Korea to urge it to disarm, but China will remain reluctant to use too much pressure. Beijing fears a collapse of fledgling leader Kim Jong Un's government and the instability and flood of refugees that could ensue. China also fears the possible emergence of a U.S. ally on its border if the rival Koreas unify.
There are no signs of major breakthroughs in the frosty relationship between Washington and Havana. The U.S. says the island must hold free elections. Cuba demands an end to the 50-year-old economic embargo. Neither side has shown a willingness to budge.
Yet freed from worrying about the voting from swing state Florida's Cuban-American community — where he polled about even with Romney — the president has room to tinker with the sanctions and their enforcement if he's interested in pursuing a thaw with Havana.
Obama could allow more U.S. travel and trade, try to increase diplomatic and law-enforcement cooperation or remove Cuba from Washington's list of state sponsors of terror, a designation that has long irked Havana.
Obama's re-election also means Cuba policy changes he made in the first term will likely remain, such as increased cultural exchanges and eased restrictions on Cuban-Americans traveling to the island and sending remittances back home. The latter has become a key source of financing for mushrooming small businesses allowed under President Raul Castro's economic reforms.
Perhaps Washington's top priority on Cuba is winning the release of Alan Gross, a U.S. government subcontractor sentenced to 15 years in prison after he imported sensitive communications equipment. Gross and U.S. officials say he was only setting up Internet connections for the island's Jewish community.
Cuba has demanded the return of five Cuban intelligence agents serving long sentences in the United States. Washington rejected that idea.
Those calling for stronger action on climate change were thrilled that Obama made a reference to the "destructive power of a warming planet" in his victory speech in a reference that clearly included the devastation by superstorm Sandy on the U.S. East Coast. Now comes the hard part: doing something about it.
Many countries are still frustrated by what's seen as a lack of ambition from the U.S. in global efforts to curb greenhouse emissions.
The Bush administration pulled out of a U.N. pact to curb emissions from industrialized countries, saying it was unfair because it didn't include major developing economies such as China
The U.S. hasn't really shifted that stance under Obama, insisting it won't be part of any global climate pact unless it also imposes binding commitments on China, which views global warming as a problem mainly caused by the West.
That issue is likely to remain a stumbling block during Obama's second term. Sweeping climate action, including international commitments, needs approval from Congress, where many Republicans don't accept the mainstream science on global warming.
Associated Press writers contributing to this report: Elizabeth A. Kennedy in Beirut, Lebanon; Deb Riechmann in Kabul, Afghanistan; Amy Teibel in Jerusalem; Matthew Pennington and Desmond Butler in Washington; Karl Ritter in Stockholm, Sweden; and Peter Orsi in Havana, Cuba.