Presidents, prime ministers and other top leaders from around the world are converging in New York this week for the United Nations General Assembly.
But amid their careful diplomatic language, there are numerous tensions lurking in the sidelines.
Here's more on the flashpoints:
The new Iranian President's first speech to world leaders toned down anti-Israel rhetoric and offered negotiations with the U.S. and its allies over the disputed nuclear program, showing a more moderate face of the hard-line regime in Tehran.
However, President Hasan Rouhani also took repeated digs at America and the West on Tuesday, much like those that were staples of his predecessor's annual messages to the UN.
There had been speculation that Iran and the United States would start to bury decades of suspicion and animosity with a handshake and an exchange of pleasantries if Mr. Rouhani and President Barack Obama crossed paths inside the UN. But the euphoria faded by midday Tuesday, when Mr. Rouhani skipped a lunch where he could have greeted Mr. Obama.
In his speech, Mr. Obama said he needs proof of Iran's goodwill before the U.S. would be willing to shift its tough stance against the country's nuclear program, a reference to harsh sanctions that Washington has imposed. Iran is seeking relief from the sanctions.
World powers have tried for years to curb Tehran's nuclear program to prevent Iran from building a bomb. But Iran insists its program is peaceful, and has long demanded that the world recognize its right under international treaties to enrich uranium – a process that can be used to produce fuel for nuclear weapons or nuclear energy.
Mr. Obama appealed to the United Nations on Tuesday to back tough consequences for Syria if it refuses to give up chemical weapons and urged Russia and Iran to end their support for President Bashar al-Assad.
Russia, Mr. Assad's main backer, said there was a "common understanding" with the U.S. on how to move toward agreement for a UN resolution that would support the chemical arms deal, but both nations said there was more work to be done.
At the same time, Mr. Obama said agreement on Syria's chemical weapons should energize a larger diplomatic effort to end 21/2 years of civil war – a sentiment echoed by the leaders of Turkey, Jordan and France, among others.
Mr. Obama stepped back from launching unilateral military action against Syria this month, setting in motion a diplomatic effort that led to Russian assistance in persuading Syria to agree to give up its chemical weapons after a poison gas attack on Aug. 21 that U.S. officials say killed more than 1,400 people.
In a bid to ensure Syria fulfills its promise, Mr. Obama's challenge at the UN was to persuade world leaders to apply pressure on Damascus with a Security Council resolution that includes tough consequences should Mr. Assad not surrender his chemical weapons stockpiles in a verifiable way.
Amid heightened tensions over Kashmir, Indian Prime Minister Manmohan Singh and Pakistan's Nawaz Sharif are expected to meet this week on the sidelines of the General Assembly.
Analysts expect the meeting will address a series of fatal clashes along the Line of Control dividing the Himalayan region between India and Pakistan, events that followed a pact by the two nations to resume stalled talks to strengthen ties.
The clashes have left dead at least eight soldiers from both countries in less than two months. The South Asia Terrorism Portal, which tracks the violence, says this year's toll is 44 members of the security forces, up from 17 for all of last year.
While the talks could soothe tension between the two nuclear powers, Mr. Singh's scope of manoeuvre on concessions to Pakistan is limited, as India heads for elections that must be held by May.
Pakistan's Foreign Ministry declined to comment on the substance of any talks, but a spokesman for Mr. Sharif said the meeting was "most likely" to take place.
Mr. Obama called for the international community to renew its commitment to a two-state solution to help end the Israel-Palestine conflict.
"The time is now ripe for the entire international community to get behind the pursuit of peace," he said.
Mr. Obama noted that both Israeli and Palestinian leaders had "demonstrated a willingness to take significant political risks," citing President Mahmoud Abbas's willingness to negotiate and Prime Minister Benjamin Netanyahu's release of Palestinian prisoners.
With reports from Reuters and The Associated Press
Editor's Note: The original version of this story stated that anti-Israel rhetoric was "absent" from the Iranian president's speech. This version has been to clarify that such language was "toned down."