Five candidates have officially declared their wish to stand for selection.
However, the best-known and most hotly anticipated has shocked the country by announcing he will not stand.
Boris Johnson made the announcement two hours after his fellow pro-Brexit campaigner, Justice Minister Michael Gove, surprised commentators by announcing his own intention to stand.
How will the winner be chosen?
Only two candidates can compete for the leadership.
Five have put themselves forward so the two ultimate candidates will have to be selected from this initial list.
The first round of voting will take place next Tuesday.
The eventual winner will become leader of the Conservative Party and the next UK Prime Minister.
Boris Johnson pulls out of race
The former mayor of London, Boris Johnson, shocked the worlds of politics and media this morning by announcing his withdrawal from the selection process.
The 52-year-old, who led the main “Leave” campaign in the run-up to last week’s EU referendum in the UK, had been favourite to win.