By Nick Assinder
Political correspondent, BBC News website
There is plenty Gordon Brown will want to do as prime minister. He has put creating affordable housing near top of his "to-do" list - but there are a number of other issues he will have to address.
The war defined the latter part of Tony Blair's premiership and Mr Brown has already signalled he wants to shift the emphasis onto reconciliation.
Iraq still dominates the UK's foreign policy concerns
However, he is not expected to speed up the withdrawal, but stick to the current timetable.
Along with Afghanistan, where conditions remain hugely difficult for UK troops, it is one area where events can easily overwhelm the prime minister.
One of Tony Blair's final acts was to agree to the EU treaty, seen by many as a back-door constitution, and rule out a referendum on it.
Mr Brown will have to steer the treaty through Parliament and avoid a major backlash from voters, who will be warned by the Tories that more power is being handed over to Brussels.
The first clash may come in October when the new EU president - Portugal - wants a meeting to approve the document.
SECURITY AND TERRORISM
Tony Blair was defeated over plans for 90-day detention without charge
The prime minister has already signalled he will move to increase the time police can hold terror suspects without charge from the current, controversial 28 days.
Previous plans for 90 days - opposed by Tories and the Lib Dems - landed Tony Blair with a Commons defeat.
Mr Brown has gone for cross-party talks in a bid to win a consensus which might eventually allow the use of phone-tap evidence in court for the first time.
Mr Brown has put it top of his agenda but has some challenges ahead, with teachers pressing for a big pay rise and threatening industrial action.
There have also been reports of white boys falling behind in school and there is continuing controversy over examination standards.
Mr Brown is also likely to face a row over university top-up fees, with many institutions wanting the power to push them above the current maximum of £3,000 a year.
David Cameron has put the NHS top of his agenda
Despite record spending on the NHS, this is one of the big headaches for the prime minister.
There is said to be a spirit of revolt among staff, with unions demanding an end to private provision.
David Cameron has also attempted to seize health as a Tory issue.
Mr Brown's idea of making the service free from ministerial control, an echo of what he did with Bank of England independence when he became chancellor in 1997, appears to have been dropped.
Nuclear energy may be making a comeback
Nuclear power is well and truly back on the agenda after the recent energy White Paper.
Mr Brown will have to decide how to proceed after a consultation period ending in October.
Any move to allow the building of new power stations will meet fierce resistance from many MPs and environmental groups.
The US President gets his own file because of the extraordinarily close relationship he had with Tony Blair.
Mr Brown may want to re-define that friendship and will undoubtedly make a visit to the White House one of his priorities.
He will also want to keep his already good relations with the Democrats - not just Mr Bush's Republicans - as they may well win the next presidential election.