Obama second term: Foreign policy challenges
The US president has not changed and neither has the complex and fragmented world he faces looking out from Washington: a Middle East in crisis; an Asia alarmed, or at the very least, ambivalent about China's rise; and old powers like Europe less confident about their place in the international system.
America's own place in the international system is in flux, with a debate raging about relative US decline and what some see as Washington's weakening influence on both friends and enemies. Here are some of the foreign policy challenges facing the newly elected president.
During Mr Obama's first presidential term it was the surge of US forces that dominated the headlines. In his next term it will be the withdrawal of US and Nato combat forces - due to leave Afghanistan by the end of 2014. This inevitably presents complex political and logistical hurdles. How much of a withdrawal will it actually be?
On present planning assumptions, considerable numbers of US and allied troops may remain to help train Afghan forces or to carry out certain specialised roles. In Iraq such plans evaporated. The new Iraqi authorities simply did not want the Americans there.
Afghanistan may well be different, but the run-up to the 2014 withdrawal could be bumpy if so-called "green-on-blue" killings of Nato personnel by their Afghan allies accelerate.
Public opinion in the US and elsewhere could turn against any significant long-term presence.
Because of the Afghanistan withdrawal, relations with Pakistan will remain crucial for Washington. Over recent years, US-Pakistan ties have oscillated between bad and worse. But this remains in many ways the key relationship in what used to be called Washington's "war on terror".
Pakistan is seen by many US analysts as a failing state. It may not actually collapse, but its dysfunctionality remains a powerful source of instability in the region. But President Obama will have to manage relations with Islamabad as best he can.
Look out for US efforts to strengthen its links with India, a bilateral relationship which, for all the talk over recent years, has not developed into quite the strategic partnership that many in Washington once wished for.
With an Israeli strike against Iran's nuclear facilities delayed, the outgoing Obama administration won an additional period for economic sanctions to take effect. These are now having some impact, though the jury is out as to how far Iran's economic woes are caused by sanctions and how much by their own government's mismanagement.
Ahead of the presidential election there were tantalising hints that Iran was eager to pursue direct talks with the United States. Might this offer a genuine breakthrough, or would this simply be another way for Tehran to try to spin out the process and potentially divide the coalition of countries backing sanctions?
Israel too goes to the polls - in late January. A new government could emerge there even more strongly committed to the idea of striking Iran. There is little warmth between Mr Obama and the Israeli Prime Minister Benjamin Netanyahu. Managing this relationship will be a crucial test for the president, who may have to deal with the consequences of any Israeli action. It could have a profound impact on relations between the US and Israel. Furthermore, if sanctions are seen to be failing or if the Iranians miscalculate, then it cannot be ruled out that Mr Obama himself may have to make a fateful choice on potential US military action against Iran.
For all the talk of the Asia pivot, the Middle East will inevitably occupy a fair share of the next president's time. Containing the overspill of the Syria crisis will remain a key strategic goal, as will containing Iran. However, it is hard to see any grand initiatives emerging in US policy towards the region, nor is it clear if there will be any attempt to revive the moribund peace process between Israel and the Palestinians.
This is a region that will remain in crisis for perhaps decades to come, torn by sectarian, tribal and religious tensions, in many places underscored by failing economies, a huge youth bulge, and a scarcity of both jobs and basic resources.
Clearly the US relationships with Egypt and the Saudis will continue to be the central pillars of its approach to the Arab world. But events involving Iran or Israel and the Palestinians could easily provoke crises at a time when Arab public opinion is perhaps more powerful, but the ability of Arab governments to deliver is even more constrained.
One crucial test for the next president's foreign policy team is to try to distinguish between different forms of Islamism in politics and establish constructive relationships with those groups willing to engage with the West.
Is China an adversary of the United States, a potential partner, or both? How to square strategic competition with the intimate economic relationship between the two powers that, to an extent, underscores the prosperity of both?
Managing relations with Beijing will depend significantly on how the new leadership there decides to frame its foreign policy. Chinese assertiveness in maritime disputes with Japan, the Philippines and Vietnam have provoked tensions and have encouraged many countries in the region to welcome Washington's pivot or re-balancing towards Asia.
But there is a danger that this could trigger a more abrasive and competitive relationship between Washington and Beijing. Leading Chinese experts tend to see America's strategic goal as containing China's rise and view Washington's actions through this prism. Strategic competition thus becomes a kind of self-fulfilling prophecy. US experts say that Washington must encourage its allies to do more in responding to China's rise, but as one expert put it: "When it comes to Asia, the US does not have the option of leading from behind."
This remains a serious general problem for US foreign policy, be it the microcosm of the Sinai peninsula or the growing crisis radiating out from Mali. Ungoverned space leaves a political vacuum into which all sorts of forces may flow. The prime threat from al-Qaeda today comes from franchises or offshoots of the organisation quartered in places like Yemen or the Islamic Maghreb, in Africa. Instability elsewhere in the region, the collapse of Syria or the return to crisis in parts of Iraq could all draw in al-Qaeda-inspired groups who might establish bases in this lawless terrain.
North Korea's unpredictable regime has a tendency to provoke crises, be it the shelling of South Korean territory or potentially a new nuclear test. Little progress has been made over recent years in re-establishing international diplomatic efforts to try to grapple with Pyongyang's nuclear programme.
After considerable instability due to the succession of a new leader in Pyongyang, will there be any margin for a resumption of diplomacy? Or will the Korean Peninsula splutter into crisis at a time when President Obama has his attention on problems elsewhere?
During the campaign debates, the Republican contender, Mitt Romney, characterised Moscow as the greatest geopolitical threat to the United States. It is hard to see quite what he meant. Russia - not least due to its veto power at the UN Security Council - has the ability to frustrate concerted action on the world stage, for example its refusal to back tough measures against the Assad regime in Syria.
Russia remains an essentially regional power rather than the global ideological and military force it became during the Cold War. In his second term as president, Mr Obama is likely to eschew grand policies like the famous - and to an extent abortive - "re-set" with Moscow, in favour of a more pragmatic approach, seeking agreement where possible.