The issues piling up on the Oval Office desk start with the American economy but quickly spread to challenges overseas. Here we look at those likely to shape the next four years.
Avoid the fiscal cliff
The fiscal cliff is the alarming nickname for $607bn (€473bn) of spending cuts and tax rises that are due to take effect in January. Mr Romney favoured scaling back proposed spending cuts, especially to the defence budget, and scrapping the tax rises. Mr Obama was keen to maintain the cuts while keeping those tax increases on families earning more than $250,000 a year. Analysts are hopeful that the threat of recession will force a compromise, but the deal is expected to be a last-ditch fudge that pushes tougher decisions on spending and taxes later into 2013.
Speed up the recovery
If avoiding the fiscal cliff is at the top of the in-tray, the economy is the biggest item in it. The world's largest economy is growing at just 2pc and unemployment is at 7.9pc. The Democrats' recovery plan involved investment in public infrastructure, new sources of energy and improving schools, while Republicans favoured cutting taxes and rolling back regulation. The US has a $16trn national debt and, while financial markets and other governments do not want to see it embarking on drastic austerity, they will want to see an agreement to rein in debt over the long term.
Heal a divided Washington
After one of the most bitter elections in recent memory, it is clear that American politics is polarised. Both Democrats and Republicans blame the other for the fissure. Whoever is in the White House needs to build a consensus that can get things done -- urgently.
Stop a nuclear Iran
The US and the European Union have introduced a series of sanctions against Iran, and there is evidence that they are taking a toll on its economy. Mr Obama has defended the policy, arguing that they need more time to work. However, whoever is in the Oval Office knows that the clock is ticking. Israel has said it will take military action against Iran if it feels that the nuclear programme is becoming a potentially deadly threat.
Withdraw from Afghanistan
The war in Afghanistan that began after the September 11 attacks has been a constant and sometimes troublesome backdrop for the Obama administration. After sending in 33,000 more troops, Mr Obama has laid out plans to withdraw all US soldiers by the end of 2014. The timetable was not a campaign issue. But even if US troops do leave, keeping an eye on neighbouring Pakistan, with nuclear weapons and a strong military, will be a priority over the next four years.
The Chinese relationship
The Asian powerhouse is America's second-largest trading partner after Canada. Mr Obama and Mr Romney spent much of the campaign trading blows on who will bring back jobs that have moved to China. Experts believe that, given the strategic importance of the relationship with China, which is the biggest foreign owner of US government debt, quiet diplomacy will quickly replace campaign rhetoric.
Hope Europe's debt crisis does not flare up
The continent's economic woes have posed the single biggest threat to the US recovery over the past two years and remain a danger. Ted Alden, a fellow at the Council on Foreign Relations, says that the most effective way the US can help Europe is to speed up its own economic recovery.
What to do in Syria?
The US has stood back from the civil war in Syria, but the approach has drawn criticism and may have to change.
Make progress on peace between Israel and the Palestinians
The pressure over the next four years to make progress towards a lasting peace will only increase. The new wave of leaders brought to power by the Arab Spring are keen to see a resolution to the conflict that has dogged US relations with the Arab world for decades. (© Daily Telegraph, London)