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Boris Johnson has promised not to make any big policy decisions that would tie the hands of whoever the Conservative Party chooses to replace him as prime minister.
Downing Street has said the government will focus solely on delivering policies that have already been agreed.
Mr Johnson is appointing ministers to fill the roles vacated by the mass walkout that helped trigger his departure.
He has insisted the government will not "take its foot off the gas" when it comes to delivering on its manifesto commitments.
But a change of prime minister always means some big challenges - and big decisions - have to be put on ice until a new team is in place at the top.
Here are some of the biggest challenges this government faces.
Tax cuts
Before this week's turmoil, Mr Sunak and Mr Johnson had a date in the diary - a major joint speech on 12 July on the economy.
Proposals being floated included a cut to VAT, income and corporation tax.
The previous Chancellor Rishi Sunak said clearly in his resignation letter that, on these issues, his approach was "fundamentally too different" to that of the prime minister's.
BBC Economics Editor Faisal Islam says that when the new chancellor, Nadhim Zahawi, was appointed there was talk of a review of all fiscal policy with "nothing off the table".
In theory, all of this is now parked while the Conservatives select a new leader. Indeed, the issue of tax and spending is likely to feature heavily in the contest itself, particularly now that Mr Sunak has entered the race.
If the Tory leadership campaign was to last a couple of weeks, then this would not matter much, says Faisal Islam. As it looks likely to last months, this could be a problem.
Cost of Living
Boris Johnson freely admits that the cost of living crisis is the biggest domestic challenge his government faces.
Before he announced his resignation, he had been expected to hold regular press conferences to highlight what the government was doing to help.
These will not now happen, Downing Street said.
Asked whether the government would intervene if the cost of living crisis worsened, the PM's spokesman said the government would not seek to introduce fiscal measures that would have a "significant impact" on the next prime minister.
He added that measures to ease the cost of living crisis - such as the cut to National Insurance - had already come into force.
Public sector pay
The rising price of things like food and petrol, have led to demands for wage increases.
Some sectors - rail workers and barristers - have gone on strike for better pay, while unions representing teachers and nurses have suggested they could also take action.
Last year, then-Chancellor Rishi Sunak pledged public sector workers would see "fair and affordable pay rises" and a public sector pay review is still going ahead, despite his resignation.
In past years, many of the decisions about the annual pay settlements have been made in the final days of July.
Pay rises below inflation could lead to strikes, but there are questions over whether a temporary government would have the power to offer above inflation increases.
With inflation at a 40-year high and heading for double digits, any decisions on this, including whether the Treasury provides the funds for rises higher than 2-3%, will not wait for the months' long completion of a leadership contest.
Northern Ireland Protocol
The government has introduced a bill to scrap parts of its deal with the EU on post-Brexit trade in Northern Ireland.
The EU were very critical saying the bill was illegal and would not work.
Tim Durrant, of the Institute for Government think tank. says: "There are strong feelings in the Tory party that the NI Protocol issue needs to be sorted and it will be a key topic during the leadership contest".
The legislation still has a number of stages to get through Parliament and that is unlikely to be completed before the autumn.
That means a new prime minister could decide to carry on with the same policy or take it in a different direction.
Channel 4 privatisation
The plan to privatise Channel 4 - announced in May - delighted some Conservative MPs, but made others feel deeply uneasy.
Culture Secretary Nadine Dorries has argued that government ownership is holding the channel back.
But the move was also likely to face opposition in Parliament, particularly the House of Lords.
A bill has not yet been introduced to Parliament and a new prime minister might decide to can it rather than face a potentially tricky battle.
What can the 'caretaker' government do?
In office but not in power? What can and can't a "caretaker government" do?
The basic principle is that the continuity Johnson administration can't pre-empt big decisions for their successor.
So no major new policies, laws, public appointments...
The trouble is - an unexpected event.
Even caretaker governments still have to govern, and possibly take urgent actions - and this one has a cost of living crisis, a war in Ukraine and a continuing pandemic crowding its in-tray.
And it may have to do quite big things in response. But non-urgent policy changes are now on hold.
The key text on this is the Cabinet Manual (the rulebook for senior ministers) which will leave top civil servants to police the grey areas around what is urgent and what can await the new leadership.
"It becomes about responsible decision-making," says Dr Catherine Haddon of the Institute for Government think tank.
It's a situation senior civil servants have to navigate when prime ministers step down, or lose a confidence vote, or call an election.