As world leaders gather at the United Nations headquarters in New York for the General Assembly, we look at the key issues that will be dominating the agenda - from the challenge of climate change to shifting security issues in the Middle East.
CLIMATE CHANGE : Richard Black, environment correspondent
The main climate-related event takes place before the opening of the General Assembly proper, at a one-day special session on climate change called on the personal initiative of UN Secretary-General Ban Ki-moon.
When the Intergovernmental Panel on Climate Change (IPCC) announced in 2007 that climate change was "unequivocal" and more than 90% likely to have a human cause, Mr Ban declared that "all humanity must take responsibility" for tackling it. In the period since, he has put the climate agenda near the top of his to-do list.
Increasing temperatures are already having an impact on icebergs
Negotiations on a new UN treaty to supplant the ageing Kyoto Protocol have been going on all year, and a number of critical obstacles remain.
Tuesday's special session is not expected to come up with any startling new policy announcements. But it should give heads of government time to discuss their priorities and their outstanding issues in a setting very different from the labyrinthine UN treaty talks.
Mr Ban hopes - as do the numerous campaigning organisations putting their supporters on the streets of New York this week - that this direct, leader-to-leader contact can remove some of the log-jam. Part of the day will be spent in roundtable sessions. Gordon Brown is due to co-chair one on climate finance.
After the special session, many of the key players will head to Pittsburgh for the G20 summit, which President Barack Obama hopes will generate a new initiative on financing poorer countries' transition to a carbon-constrained future.
The following week, UN climate treaty negotiations resume in Bangkok. Mr Ban, and many others involved, will be hoping that the New York or Pittsburgh summits can unstick that troubled process.
AFRICA : Martin Plaut, Africa analyst
For African leaders two events are already on the agenda - the launching of an initiative on malaria and organising a unified African position on climate change, ahead of the Copenhagen meeting in December.
Some African states want sanctions against Sudan's president lifted
Heads of state and government from 10 African nations will meet on 23 September to announce the formation of an African Leaders Malaria Alliance to try to reduce illness and deaths from the parasite.
The initiative is being led by President Jakaya Kikwete of Tanzania. Malaria is one of the biggest health and economic challenges to Africa, accounting for one quarter of all deaths of children under five, and costing the continent around $12bn a year.
Ethiopian Prime Minister Meles Zenawi, who is co-ordinating Africa's response to climate change, will use the General Assembly to lobby for the continent.
He has already warned that African nations will not rubber-stamp a new climate change treaty to replace the Kyoto Protocol unless it takes account of the continent's specific interests.
Some African states are also likely to lobby for the lifting of sanctions against Zimbabwe's President, Robert Mugabe, and Sudan's Omar al-Bashir. And then there is always the chance to deal with other bilateral issues, as well as popping out to do a spot of shopping in some of New York's better stores.
MIDDLE EAST : Jeremy Bowen, Middle East editor
The Middle East is one of the major issues on the agenda at the UN General Assembly this week.
On Tuesday, President Obama will hold a series of meetings with the Palestinian President Mahmoud Abbas and the Israeli Prime Minister Benjamin Netanyahu.
The continued building of settlements is a major obstacle to starting talks
President Obama wants new peace talks about the setting up a Palestinian state alongside Israel. But his plan has stalled over Israeli construction of homes for Jews in the occupied Palestinian territories.
Israel's refusal to stop building in the Jewish settlements - all of which are illegal under international law - despite repeated American requests, means that the Palestinians will not renew negotiations.
President Obama's envoy Senator George Mitchell tried for months to make a deal. Now it is up to the president himself.
Mr Obama has defined peace between Israel and the Palestinians as a national interest of the US. But the failure so far to restart peace talks is a serious and potentially humiliating setback for him. President Obama needs to find a way to turn his meetings with the Israeli and Palestinian leaders into more than just photo opportunities. He cannot afford to let his ambitious plans for the Middle East fall apart so soon.
The controversy over whether or not Iran is building a nuclear weapon - and, if so, what to do about it - is the other big issue in the Middle East. Israel will stress to the Americans that they should worry less about the settlements and the Palestinians and more about Iran. The Americans believe that progress on the Israel-Palestinian track would make it easier to deal with Iran.
Iran's President Ahmedinejad is scheduled to address the General Assembly - and the permanent members of the UN Security Council plus Germany meet to prepare for vital negotiations with Iran next week.
SECURITY : Jonathan Marcus, diplomatic correspondent
President Barack Obama's speech last April in Prague has been described as "the most important statement on nuclear weapons policy in a generation". There he set out his administration's commitment to seek a world without nuclear weapons.
Prague was a strategic choice for a major foreign policy speech
He accepted this was a vision that might not be achieved in his lifetime. But in New York he intends to take the first important steps down this road.
On 24 September, Mr Obama will become the first US president to chair a meeting of the United Nations Security Council. On the agenda, a US-drafted resolution dealing with the whole question of nuclear non-proliferation and disarmament.
The text marks Washington's return to the mainstream of arms control after the unilateralism of the Bush years. The US draft resolution recommits the United States to multilateral action; support for the Comprehensive Test Ban Treaty and for so-called "negative security assurances"; guarantees by nuclear weapons states not to attack non-nuclear armed countries with nuclear weapons.
The US draft also, importantly, asserts that the rights of states to pursue peaceful nuclear energy should depend upon their willingness to fulfil their other non-proliferation obligations.
President Obama's aim is to demonstrate renewed US commitment to disarmament ahead of next year's important review of the Non-Proliferation Treaty (NPT).
While the US Senate is unlikely to have ratified the Test Ban Treaty by then, Mr Obama hopes that his work at the UN, along with the improved chances for a new arms reduction treaty with Russia - enhanced by his recasting of US missile defence plans - will lead to an agreement to bolster the NPT, which remains the corner-stone of international efforts to prevent the spread of nuclear arms.
IRAN AND THE US : Paul Reynolds, world affairs correspondent
Iran is on the international agenda because it is refusing to comply with the orders of the Security Council to suspend the enrichment of uranium and the US and its allies want to impose further sanctions on it.
Friction with Iran over its nuclear programme will cast a shadow
In particular, they would like restrictions on investment in Iran's oil and gas industry and on the export to Iran of refined petroleum products, of which it is short. However, it is not clear if any such sanctions will be imposed by the UN itself or whether, because of Russian and Chinese reluctance, individual countries or groups will look at doing this themselves.
Iranian President Mahmoud Ahmadinejad is bound to be listened to closely when he speaks. Iran is meeting the permanent members of the Security Council plus Germany after the General Assembly on 1 October.
In a rare move, President Obama will chair a special meeting of the Security Council. His speech will probably confirm a US rapprochement with the UN after the Bush years and he can expect an enthusiastic reception. His decision to shelve the anti-missile defence system in Eastern Europe will also reduce tensions with the Russians, whose President, Dmitry Medvedev, he is to meet.
But President Obama is also likely to press the case for sanctions on Iran so the Iranian issue will continue to cast a cloud over the General Assembly session.
AFGHANISTAN : Martin Patience, Kabul correspondent
The issue of Afghanistan will be centre-stage at the UN General Assembly. Security in the country is deteriorating in the face of a strengthening insurgency; the government is largely seen as corrupt; and a deeply flawed election has yet to be resolved.
Western diplomats are now admitting Afghanistan might be a failure
Earlier this week, the top US commander in the country, General Stanley McChrystal, wrote in a leaked report that unless more US troops were sent to the country, the mission risked failure.
But there are concerns because of mounting foreign casualties - and the controversy surrounding the election - that the US Congress and other countries will not wish to send more troops to the country.
And there is growing concern that the Afghan government is simply not delivering - mostly because of corruption, but also because it has not received enough support from the international community.
The UN special envoy to the country, Kai Eide, is expected to tell Congress that now is "decision time."
He wants to see greater co-operation between various countries - and a clear set of objectives agreed upon - in a mission that most observers say has been muddled.
Eight years after the overthrow of the Taliban, the movement is strengthening across the country. Western officials admit that without resolve the international community could lose in Afghanistan.
And they fear, that in victory, the Taliban and other groups such as al-Qaeda, would then use the country to further destabilise the region.