As Barack Obama is sworn in, our BBC correspondents look at what his presidency will mean for the rest of the world.
Karen Allen, KENYA
Barack Obama's ancestral village has been ignited by celebration.
Thousands have thronged to join in the festivities and to dance under a massive banner, which simply reads "congratulations our son, our hope".
Although many from the Obama family were in Washington to witness the swearing-in, their neighbours here in western Kenya watched it on massive TV screens, and all have high expectations for the new Obama administration.
Others like Vitalis Akech Ogombe, who was in charge of some of the festivities, told me that they hoped the first African-American president will reign in the continent's leaders who have strayed away from democratic ideals.
''Obama as president is going to transform Africa particularly, and those who are still dictators should know that we should practice proper democracy,'' he told me as he watched the inauguration.
Never has US politics mattered so much to the people of Africa.
But this evening the swearing-in of the first African-American president has infused hope into the hearts of millions of people across the continent.
Although Washington is thousands of miles away tonight, it feels like the world is a smaller place.
John Sudworth, SOUTH KOREA
It was the middle of the night here when the new US president took his oath of office, so there was little sign of any anticipation on the streets of Seoul. And the pictures of the ceremony vie for front page space in this morning's newspapers with dramatic shots of the fire that claimed six lives in central Seoul on Tuesday.
The new president will have to decide in which direction to push the long-running negotiations aimed at persuading North Korea to give up its nuclear weapons
Nonetheless, the coverage and commentary will leave readers in no doubt that an Obama presidency will have important implications for the Korean peninsula.
In the coming months, the US and South Korean legislatures will need to ratify a free trade agreement, a long-running source of political tension here. And crucially, the new president will have to decide in which direction to push the long-running negotiations aimed at persuading North Korea to give up its nuclear weapons.
The Bush administration hands over a mixed set of results.
It was under the former president's stewardship that North Korea tested its first atomic weapon in 2006, but the subsequent return to dialogue has brought some progress, notably the shutting down of its key nuclear reactor site.
Many analysts believe Pyongyang may be keen to test the new administration by stoking regional tension, and this could be one major foreign policy challenge that comes early for Mr Obama.
In North Korea itself there was no mention of Mr Obama's inauguration, our Seoul correspondent adds.
More than 12 hours after the ceremony, none of the strictly controlled state media - print, radio or television - had mentioned the event. Space was found in the ruling party broadsheet for the news that the president of Equatorial Guinea recently received the North Korean ambassador, but there was no room for Mr Obama.
North Koreans, however, will be aware that he is the new US president as the election result was reported in November, albeit three days late.
Analysts say that North Korea's New Year message was much less hostile towards the United States than in the past, possibly a signal that Pyongyang is withholding its judgement on the new administration.
But, at the same time, it has been ratcheting up the tension with South Korea. A senior military officer recently delivered a statement on state television threatening "all-out confrontation" with the south.
Michael Voss, CUBA
The inauguration did not make headline news on Cuban television but it was reported along with references to Martin Luther King and advances in civil rights.
There is widespread anticipation that the Obama presidency could lead to a period of engagement rather than confrontation.
No-one is expecting that President Obama will move quickly to lift the decades old trade embargo
Former leader Fidel Castro recently described the new US president as a decent man. His brother, President Raul Castro, said that he appeared to be an honest man.
No-one is expecting that President Obama will move quickly to lift the decades old trade embargo.
But there are real hopes that he will fulfil his campaign promises to ease restrictions on Cuban Americans visiting and sending money to relatives back home.
That he can do through a presidential decree. Ending the embargo would need a change in the law and congressional approval.
There are still huge stumbling blocks to normalising relations. On the campaign trail Barack Obama made it clear that this depended on moves towards greater democracy and the freeing of political prisoners.
Raul Castro recently offered a prisoner exchange for five Cubans serving long sentences in the US for spying. He also said that he would be prepared to hold direct negotiations with President Obama providing there are no preconditions.
James Reynolds, CHINA
Bad news for President Obama. The one country which may decide America's future prosperity was asleep when he took the oath of office.
It is not anyone's fault. The framers of the US Constitution did not have a peak time Chinese TV audience in mind when they drew up the presidential inauguration time.
Mr Obama was sworn in at 0100 China time, by which time most people here had already gone to bed
Mr Obama was sworn in at 0100 China time, by which time most people here had already gone to bed - from my apartment window, I could only pick out a handful of lights left on across the city.
For those who did stay up to watch the inauguration, there was brief coverage on China state TV's news channel. Those who can afford a satellite dish got to watch more extensive coverage on a Hong Kong news channel.
In normal waking hours, China has shown a great deal of interest in Mr Obama.
We have collected and translated a few comments from Chinese Internet users.
"Martin Luther King should be very happy in heaven. His phrase 'I have a dream' goes into reality! America is a great country," said one.
"Obama will certainly limit the import of China's goods and appreciate Chinese currency in order to realise his promise to the unemployed people in America. He will not necessarily be good to China," said another.
"After all he is the American president. He was elected at the time of economic crisis. How will he solve such complicated domestic and overseas problems, we have to wait and see."
While another wrote: "To our middle-age friends, get your children to attend schools in America. Your grandchildren could have a chance to be American president! To our young friends, go to study in America, maybe your son could become the American president. This is the spell of America."
Lucy Williamson, INDONESIA
There is quiet jubilation in the Indonesian capital tonight. Jubilation that George Bush has gone, and that now Indonesians have - as many see it - a man in the White House who understands them.
Many are sure that the four years he spent in Indonesia shaped his world view
At the Democratic Party celebrations, hundreds crowded around the video screens - researchers, IT workers, his former classmates, his fans.
And out on the streets of Jakarta too, everyone knew the story - how the man now entering the White House used to live in a very ordinary house indeed, in an ordinary Indonesian neighbourhood just a short drive away.
The ordinariness of Barack Obama's childhood here has impressed Indonesians. Many of them are sure that the four years he spent in Indonesia shaped his world view - that we are going to see very different American policies on Iraq, Afghanistan, the Middle East - a new approach, in fact, to the Muslim world.
He will be met with high expectations here - as elsewhere. And running through it all is a huge sense of pride, a feeling shared by many Indonesians that, as one man put it, Barack Obama "somehow belongs to us".
Tim Franks, JERUSALEM
Barack Obama is a source of intrigue, and a repository of hopes, in this part of the Middle East.
There is, to begin, a sense of what he is not: he is not George W Bush, the president often described as "Israel's best friend".
For the new president to make an impact, he will need to engage early
Mr Bush made centre-right Israelis swoon - he repelled most Palestinians.
That is not to say Israelis or Palestinians expect the pendulum to swing in perfect symmetry.
But writing in Israel's Haaretz newspaper, Zvi Bar'el says that Mr Obama's commitment to Israel's security, while as deep as that of Bush or Clinton, may be founded on a different vision: the importance of peace.
"This may be novel, and perhaps even revolutionary in Israeli eyes," he writes.
There is agreement among Israelis and Palestinians that for the new president to make an impact, he will need to engage early.
Most Palestinians, whether in the West Bank or Gaza, will tell you that the re-cooked peace process, under President Bush, has only pushed the prospect of statehood further away.
Rana Sabbagh, a Jordanian newspaper columnist, says that President Obama will have only a few months to show progress on building a Palestinian state.
Otherwise, she writes, "the popularity of Hamas and the resistance axis will grow".
Both sides concede though that international involvement can only go so far.
Much will depend on the outcome of Israel's general elections, in three weeks' time, and Palestinian efforts to end their own toxic splits.
Jonny Dymond, IRAQ
Much of Barack Obama's early electoral support was based on his opposition to the Iraq war and his promise to withdraw US combat troops.
Now he faces the challenge of making good on that pledge.
The good news for the new president is that the wind appears to be blowing his way.
The challenge for the US now is to manage an orderly transition
US troops are off most of the streets of Iraq's towns and cities - violence is down on a year ago, sharply down when compared to 2006 or 2007.
And the Iraqi army and police, aided by semi-official militias have pacified swathes of territory once under the control of militants.
The challenge for the US now is to manage an orderly transition.
There are still significant obstacles ahead - there are three sets of elections this year - violence often precedes such polls in Iraq.
There is no political agreement yet over oil revenue sharing.
It's not clear what will happen to members of Sunni militias that have done so much to curb militant violence, once the US stops paying them.
The relationship between the Kurdish north of Iraq and the Arab centre and south is still fractious.
And some of the country's neighbours still have the power to destabilise a fragile situation.
Barack Obama will have to balance his desire to withdraw US troops against progress made on complex diplomatic, political and security fronts.
Jon Leyne, IRAN
Iran is one country certainly not gripped by inauguration fever.
Many Iranians are hoping that the arrival of a new US president will improve relations between Iran and the United States.
Within ruling circles there's a cautious approach, waiting for President Obama to make the first move
And almost everyone here will be hoping for a new approach on the Israeli-Palestinian conflict - but Iran today is a country in the grip of a growing economic crisis.
For most people, all their energy is required simply to earn a living - and it could get dramatically worse following the collapse in the price of oil - Iran's main source of revenue.
After Mr Obama's election victory, President Mahmoud Ahmadinejad of Iran sent him a message of congratulations.
But since then, the signals from Tehran have been less encouraging, and in recent days the anti-American rhetoric has been as tough as ever.
Within ruling circles there's a cautious approach, waiting for President Obama to make the first move.
Washington may also be tempted to wait before launching any diplomatic initiative, in order to see if President Ahmadinejad is re-elected in Iran's presidential election this June.
But the hawks will argue that dealing with Iran is urgent, as the Islamic Republic moves ever closer to the ability to make a nuclear bomb.
Rupert Wingfield-Hayes, RUSSIA
As virtually the whole of the world stops to watch and celebrate with America today, there is one place that seems determined to play the role of party-pooper.
In Moscow indifference seems to be the overwhelming emotion.
Russia is going to be one of the trickiest relationships for the new American President to handle
Indeed in a BBC worldwide poll Russians have come out as the least optimistic that President Obama will improve US relations with the rest of the world.
Perhaps it's just that Russians are more realistic, or maybe it's a reflection of the famously gloomy Russian soul.
Few doubt Russia is going to be one of the trickiest relationships for the new American president to handle.
The Kremlin still views diplomacy as a zero sum game - any American gain is a Russian loss.
For the last 20 years the tide of history has flowed in Washington's direction.
But now, with its new-found oil wealth, Moscow is determined to turn the tide, and reassert its influence, particularly over its "near abroad" - that means countries like Georgia, Ukraine, Belarus and Moldova.
No-one expects President Obama to dump America's new allies in Tbilisi and Kiev, or to suddenly scrap plans for missile defence in Poland and the Czech Republic.
Clearly no-one should expect a sudden thaw in the icy relations between Washington and Moscow.
Steve Rosenberg, GERMANY
Chancellor Angela Merkel may have got on pretty well with George W Bush (remember the public back massage he treated her to at a G8 summit?).
But most Germans can't wait to see the back of a US president they believe has made the world less safe.
As the crowds shouted "Yes we can!" it was clear then who most Germans wanted to win the White House
In contrast, Barack Obama is already supremely popular in Germany, because, first, he's not George Bush, and, secondly, his message of change has struck a chord with the German public.
"Obamamania" infected Germans last year ahead of the American elections.
When Mr Obama visited Berlin in July, more than 200,000 people gathered to hear his speech.
As the crowds shouted "Yes we can!" it was clear then who most Germans wanted to win the White House.
But under President Obama, a number of issues could cause friction in US-German relations.
Mr Obama would like German troops to assist Nato combat operations in southern Afghanistan.
But Germany has no desire to move its soldiers from less volatile northern Afghanistan to a battle zone.
There may be differences of opinion, too, over the economy. Chancellor Merkel has already warned Washington not to prop up the ailing US car industry with billions of dollars of subsidies - fearing Germany's car industry could be disadvantaged.