No party has been able to secure an outright majority in the House of Commons and, after four days of frantic negotiations between the parties, the shape of the next government is still not clear.
The situation is described as a
with no single party having enough MPs - 326 - to win parliamentary votes without the support of members of other parties.
Sinn Fein's five MPs are not included in these coalition scenarios as they traditionally do not take up their seats. Technically, however, 326 remains the figure needed for an overall majority. The seat of Thirsk and Malton is also not included as the election there was delayed due to a candidate's death.
WHICH PARTY CAN TRY TO FORM THE GOVERNMENT?
The Conservatives won the most seats - 306 - and votes, but the largest party does not automatically have the right to try to form an administration.
Both the Conservatives and Labour are negotiating with the Lib Dems - who effectively hold the balance of power - about trying to form a functioning government which could win the support of a majority of MPs in Parliament.
As incumbent prime minister, it is Gordon Brown's duty to stay in office until it becomes clear which party or combination of parties can command the most support in the new parliament.
"We must always have a government, and until a new government can be formed the present government carries on," explains Professor Robert Hazell, from the Institute for Government.
Conservative Edward Heath
stayed in power for four days after the election trying to put together a coalition, even though Labour had more seats.
Gordon Brown has said he hopes to negotiate a coalition government with the Lib Dems and - if that happens - he will stand down once a new Labour leader is chosen, which is likely to be by September.
HOW MIGHT AGREEMENT BE REACHED?
During the election campaign, Lib Dem leader Nick Clegg repeatedly said the party with the "biggest mandate" - in terms of the number of seats and votes won - should get the first right to try and form a government.
The Liberal Democrats opened formal talks with the Conservatives on Saturday after Tory leader David Cameron made "a big, open and comprehensive" offer to them to play a role in forming a "strong and stable government".
Although talks are still continuing, Mr Clegg said on Monday that they had not reached an agreement and he wanted to open parallel talks with Labour.
The Conservatives and Labour are both offering the Lib Dems a role in a coalition government, where senior Lib Dem figures would sit in cabinet and shape policy.
They are also both offering potential changes to the electoral system - one of the Lib Dems' key demands - although the Labour proposal on this goes further.
Professor Hazell says the Liberal Democrats are, in effect, setting the terms of negotiation.
A combination of the Tories and the Lib Dems would be the only arrangement with clearly more than 326 seats, although the BBC's Political Editor Nick Robinson said many Lib Dem MPs and activists felt an aversion to any deal with the Conservatives.
Even if Labour and the Lib Dems got together, they would fall well short of a majority and would need to rely in key votes on smaller parties in Northern Ireland, as well as potentially Plaid Cymru in Wales and the Scottish Nationalist Party, supporting them or not voting against them.
Critics - including some within Labour ranks - say a government of this kind would be inherently unstable and could collapse at any time.
But Dr Tim Bale, lecturer in politics at Sussex University, believes a so-called "progressive" alliance is feasible as they could argue that together they have secured nearly 55% of the vote.
"If the Lib Dems play it cleverly, they can actually present this as the majority solution for Britain and a much more stable solution than a Conservative minority government," he adds.
The terms of any Lib Dem deal with either party would have to be agreed by 75% of both the party's MPs and its federal executive - made up of officials and party members.
WHERE DOES THIS LEAVE GORDON BROWN?
If Mr Cameron gets the support of the Lib Dems, it is expected Mr Brown would concede and resign as prime minister.
The Queen would then invite Mr Cameron - as current Leader of the Opposition - to try to form a government.
Mr Brown has said he wants to forge a "progressive" alliance with the Lib Dems around areas of common agreement such as financial stability and voting reform.
However, it is thought the Lib Dems were not willing to do a deal with Mr Brown as leader.
Mr Brown has now said he will stand aside in a couple of months and be replaced by another Labour politician, which makes the prospect of a deal more likely.
But critics have said any new leader will lack legitimacy - not having been leader during the election - and there could be a second prime minister in a row not to have been chosen by the public.
BY WHEN MUST THE GOVERNMENT BE FORMED?
Politicians from all parties say a decision must be taken as "quickly as possible", acknowledging that the next 24 hours are likely to be crucial.
There is no formal deadline for when an administration must be formed but a key date is 25 May, when the Queen's Speech is due to set out the government's priorities during the parliament.
Professor Hazell says while the public is used to elections being over in a day or so, negotiations to form a government in a hung parliament could take between a week and 10 days.
However, amid concerns about the economic situation across Europe and financial market volatility, the parties have come under some pressure to reach some accord within days.
In the past few days, the role of the civil servants has been crucial in smoothing talks between the parties.
Earlier this year, the Cabinet Secretary Gus O'Donnell drew up a document on how civil servants would help with these discussions.
They are not allowed to provide policy advice but can show where policy overlaps.
IMPORTANCE OF QUEEN'S SPEECH ON 25 MAY
A minority administration must show it has the confidence of the Commons, but the Queen's Speech does not have to be the deadline for negotiations between parties.
The administration may put forward a slimmed down legislative programme which it believes is more likely to gain support.
But if it loses the vote on the Queen's Speech this would be seen as a "no-confidence" vote and force its resignation.
EARLY SECOND ELECTION?
If no agreement can be reached between parties and no government is unable to command enough support to get the Queen's Speech through parliament, there would be a need for a second election.
However, party leaders may not be keen to go to the polls again unless the opinion polls indicate voter intentions have changed markedly. Parties would also consider the fact that another election would be costly financially.
Ms Fox says "the country would not readily forgive them for forcing a second election", and says the parties, mindful of that, will be likely to strike a deal.