US Secretary of State Colin Powell vowed after President Bush's re-election that his country would continue to pursue an "aggressive" foreign policy during the next four years.
But how hawkish will this administration be in its second term? What are the key challenges that it faces, and how is it likely to deal with them? We asked six prominent foreign policy analysts for their views.
Ted Galen Carpenter writes about defence and foreign policy at the libertarian Cato Institute.
Secretary of State Colin Powell put it very well: this election was a mandate for President Bush's foreign policy, which is likely to be quite aggressive. First on the agenda will be nuclear proliferation in North Korea and Iran.
On North Korea, the attitude of powerful US allies, particularly Japan and South Korea - plus China and Russia urging restraint - might inhibit US military action, but this president has demonstrated time and again that he is willing to act in the face of opposition.
And, if diplomacy fails to get an agreement with Iran that the US regards as adequate, then the prospect of military action there is very possible. Any response would be overwhelmingly an air response against sites related to Iran's nuclear programme and other assets - the US isn't going to invade Iran. The public would be very uneasy, but on the other hand, negative attitudes towards the Islamic government in Iran are virtually imprinted on the American DNA since the 1979 hostage crisis.
Relations with Europe are likely to remain tense, especially if there are sharp differences over the Middle East and Iran, and especially if the US continues to muddle about in Iraq without any definitive solution. The Europeans seem to have taken the attitude that if Bush were defeated everything would go back to the way it was before. Now they know he is going to be in office another four years, but also they sense that there are rather significant ideological and cultural differences that make it very difficult to maintain the close alliance.
Stefan Halper worked in the Nixon, Ford and Reagan administrations. He is author of America Alone: Neo-conservatives and Global Order.
George W Bush's electoral margin - 3.5 million votes - suggests that he will gravitate towards keeping the neo-conservatives in many key positions. But that doesn't mean there will not be policy reviews, particularly in areas where policy has already proved problematic, such as Iraq.
Foreign policy will come down to how Bush wants to be remembered - and that is as someone who fostered democracy in the Middle East and brought peace. He will not want to be remembered as having ignited World War IV or the man who left the Middle East in tatters.
However, in conducting his foreign policy, there will be a struggle between Bush's mandate, which is supported by a large number of evangelical votes, and the legacy he will want to leave. There is a narrow path to be trod.
In terms of any other possible military action, the administration will be limited. The United States already is over-stretched militarily and financially.
There is also a general weariness in America for another Iraq situation, particularly as Iraq, itself, is not going well.
Joshua Muravchik is a scholar with the conservative think-tank, the American Enterprise Institute.
Nuclear weapons and Iran is the key concern. It would be excellent if the Europeans, the IAEA could sort this out - and indeed there has been talk of this being a way of establishing unity between Europe and the US. But it depends very much on how this develops - after all you cannot unite over something that is not working. And if it does not, I think there is a very good chance of strikes on nuclear facilities. The Iranians have been very obdurate, making military action a real possibility.
It is really on the Israeli-Palestinian front that prospects are brightest. Europeans always accuse America of disengagement from the Middle East, but that is a false charge. The peace process hit a brick wall whose name was Yasser Arafat. Israel's planned withdrawal from Gaza had already opened up new possibilities, and that was before the demise of Arafat, which multiplies those exponentially.
There are at least two Palestinian leaders emerging with whom the Americans could do business. Bringing about an Israeli-Arab peace would work wonders for America's image in the Middle East, and thus help with persuading the people of the region of the benefits of democracy. And the other aspect to note is that even if this fails, and Hamas emerge on top, US-European relations would probably improve dramatically, united in their opposition to terrorists.
Steven Everts is the director of the transatlantic programme at Centre for European Reform.
As far as the Bush administration is concerned, their approach to international affairs was vindicated by the election. It is seen as a mandate to press full steam ahead.
Having said that, over the past year, we have already seen a more conciliatory attitude towards Europe. There is a cost of not working together. At a practical level for instance, the Americans have had to shoulder the costs of reconstruction and policing in Iraq. But more broadly the US needs European support to endow it with legitimacy, and even some of the most-right wing thinkers in America accept that.
From the European perspective, poor relations with America have prevented meaningful dialogue, and that puts severe constraints on what can be achieved on the international stage, particularly with the Israeli-Palestinian issue and Iran. Tehran has little incentive to respond to European pressure over nuclear weapons if it thinks that America will strike it anyway.
I expect Iran to be the top issue on the agenda between America and Europe in this second term, follow by the Israeli-Palestinian issue, and then Kyoto. Europeans take global warming very seriously and are very anxious to move towards lowering carbon dioxide emissions. It's not just about getting America to back the treaty, but pressing for some kind of concessions, and indeed you do already see some movement, a tiny opening.
The inflammatory rhetoric will doubtless continue from both sides - whether it is Jacques Chirac in France or Donald Rumsfeld in the US. But ultimately, national interests will set boundaries on how far this can go.
Joseph Nye, a former assistant secretary for defence in the Clinton administration, is dean of the John F Kennedy School of Government at Harvard.
Iran and North Korea are going to be the largest items on the agenda, along with trying to move along the Middle East peace process.
I interpreted Colin Powell's recent interview about foreign policy as a warning for people not to have expectations that the second term of Bush's foreign policy will be dramatically different from the first. But I do think there will be significant differences.
For example on Iran and North Korea, two of the countries that President Bush put on his axis of evil, he is now following a multilateral approach. He is working with the Europeans and the IAEA in the case of Iran, in the case of North Korea, the six party talks.
I think the prospect of an invasion of Iran or North Korea is very slim. There is nonetheless always some threat of force lurking in the background for Iran - although it may not be America. The Israeli Defence Minister has said that Israel would not accept Iranian development of nuclear weapons. But the idea of an invasion is really out of the question - the Americans are stretched in Iraq.
That does nonetheless leave open the prospect of bombing nuclear facilities. That is always a possibility, but when you do not know where all the facilities are, you cannot be sure of success and Iran could retaliate by stirring up trouble for the Americans in Iraq.
David Makovsky is a Middle East analyst at the Washington Institute for Near East Policy
I really believe that President Bush sees the death of Yasser Arafat and the disengagement plans for Gaza as an opportunity to re-engage.
The president thinks the US and other countries, such as the so-called quartet - US, Russia, the UN and the EU - should work together to ensure that the transition time for the Palestinians could cement the prospect of peace for the Israelis and Palestinians.
The months ahead will definitely see US engagement in this transition period. The US administration will try to demonstrate to the new leadership that there is hope.
It will engage in efforts to secure a ceasefire, work towards a co-ordinated withdrawal from Gaza, and assist with elections. It will also engage in confidence-building economic strategies.
Mr Bush believes that if these steps are successful, they will lay the foundations for implementing the road map and then lead to final status negotiations.
That will, however, be quite a long way down the road.
What do you think about the possible direction of US foreign policy? What other issues do you think may feature on the agenda? Please use the form below to tell us your views.
I believe the US will eventually strike at what it has named rogue nations, North Korea, Iran and Syria, and rightly so. For too long have these nations political regimes posed a threat to world peace.
Marc Woodhall, Derby, England
No-one, not even Bush, knows what his foreign policy will be like in the next four years. Before being elected, Bush wanted to withdraw US forces from political hotspots, such as reducing its troop commitments in Kosovo. A new period of US isolationism was expected. Today, Bush is preaching a doctrine of single-handed unilateralism, to spread democracy around the world. The fact is that his foreign policy has been a conglomeration of event-driven responses to the 11 September 2001 attacks and his own personal grudge against the regime of Saddam Hussein.
It has been far from consistent and principled. Had Mr Bush been truly committed to spreading democracy and solving the Palestinian problem, he would have made it one of his top priorities long ago, rather than presenting a hastily drawn roadmap in the midst of the Iraq war. The US will remain tied up in the mess that is now Iraq, and Bush's foreign policy priorities are more likely to depend on unpredictable events in the future, as well as on the advisers he appoints in his new cabinet.
George Saravelos, Cambridge, UK
I think the USA should put right the mess they have created in Iraq first, before they even consider invading another country. An apology to the Iraqi people also, by the USA, should also be given. I have an Iranian wife, and under no circumstances would I approve of any military action against her country. I would protest so much against any action in a way that I would even consider going to Iran to fight against the Americans!
Michael Neill, Hull, United Kingdom
I'm a supporter of the US foreign policy in the fight against international terrorism. The president's success against his democratic opponent was the first move for the continuation of the fight against terror. I feel that the US policy abroad will enable the world to maintain perfect peace as they will not give any chance to terrorist groups to prepare themselves. North Korea and Iran must co-operate with the UN inspection team if they do not want more international pressure.
Mohamed Junior Marah, Conakry, Guinea
My greatest fear is that, if President Bush truly means to "stay the course" and pursue an aggressive foreign policy (let's be honest and call it what it is - imperialistic), he'll call for a new draft, as his military (especially the Army) is too small even to serve as a bluff if he wishes to us it thusly against countries like Iran, North Korea, or Syria. Bringing back a draft would be politically disastrous for the Republican Party, yet I can't see them denying the president his wishes in the Congress. Ah, well, que sera, sera.
Paul D Alexander, La Grange, GA, USA
A 51% popular vote for President Bush is hardly to be construed as a "mandate" for Bush's foreign policy, or for that matter his other legislative initiatives. It should be observed that this 51% vote for George Bush is not 51% of the adult registered voters, even more reason not to construe it as a mandate or that half of the American adult population supports him and his foreign policy.
Thomas Grimms, AICP, Orlando, Florida, USA
The only reason why I don't think that Bush will be able to wage a few more wars is that he lacks the resources. If the US has so much trouble in Iraq against a country that had sanctions for so many years imagine what trouble it would have against Koreans one million strong army or against Iran's fanatic troops.