More than 130 heads of state and government are due to start speaking at the UN General Assembly in New York on Tuesday.
These will be the main topics on the agenda as the summit begins.
There is no specific debate about the 30-month-old Syria conflict at the UN General Assembly but it will be raised by nearly every king, president, prime minister and foreign minister who speaks.
UN leader Ban Ki-moon, who says the UN Security Council is gripped by an "embarrassing paralysis" over the war, wants the focus on efforts to call a peace conference and help for the two million refugees in neighboring countries and millions more running out of food, water and shelter inside.
Attention will focus, however, on a Russia-US plan to get chemical arms away from President Bashar al-Assad. If the Organization for the Prohibition of Chemical Weapons approves the plan, the Security Council could overcome its divisions and approve a resolution by the end of the week, giving the plan legal force.
Ban, US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov are expected to meet on Saturday to try to fix a date for a new peace conference in Geneva, possibly in October.
A picture of US President Barack Obama shaking hands with his Iranian counterpart Hassan Rowhani would flash around the world -- if it happens.
The two will be in the UN General Assembly hall on the same day Tuesday and they could both attend a lunch being hosted by Ban.
Rowhani is signalling that he wants talks with the West in a bid to ease four rounds of UN sanctions imposed over Iran's nuclear program.
Despite Rowhani's declaration that Iran will "never" build a nuclear bomb, Obama and other western leaders are waiting to see a sign of serious intent from the new government in Tehran, experts say.
The US administration is not saying whether it will risk a handshake. But the foreign ministers of Britain, China, France, Germany, Russia and the United States are to meet this week their joint campaign to end the nuclear showdown.
Special ministerial meetings will be held on the sidelines of the General Assembly on the decades old strife in eastern Democratic Republic of Congo and mounting concerns about neighboring Central African Republic.
Ban will bring African ministers together on Monday to press them to renew a political accord signed in February on ending meddling in DR Congo's affairs.
There is also mounting pressure on African government to beef up an international force in Central African Republic where a rebel takeover has left a new refugee crisis and country on the verge of anarchy.
In the optimism of the turn of the century world leaders vowed to cut extreme poverty by half and drastically improve other chronically bad health and education statistics by 2015.
In the austerity of 2013, there is less hope that the eight targets will be met. The UN leader is again having to step in to organize a series of ministerial meetings at the summit to reinvigorate efforts up to 2015 and set an agenda for a new campaign after.
A visa application to the US government by Sudan's President Omar al-Bashir, who is wanted by the International Criminal Court on genocide charges, so he could attend the UN summit caused diplomatic panic in Washington and at the UN.
The US administration is refusing to say whether it will carry out an ICC request to arrest Bashir if he makes the trip. The Sudanese president is due to speak to the assembly on Thursday.
There has been an outpouring of sympathy for Kenya's President Uhuru Kenyatta after the Nairobi shopping mall attack by Somali militants that left dozens dead. But Kenyatta withdrew from a trip to the assembly as he also faces an ICC warrant.
Other African leaders are expected to renew attacks on the international court's focus on Africa at a ministerial meeting on Thursday.