Theresa May's stepped down as leader of her Conservative party, triggering the contest to find her replacement.
That person automatically becomes Britain's next prime minister.
Their challenge will be to pick up the reins on Brexit.
So how does the process work?
Reuters' William James.
(SOUNDBITE) English, REUTERS POLITICAL CORRESPONDENT WILLIAM JAMES, SAYING:
"There are a lot of people who want to be Britian's next prime minister, and the process of choosing the prime minister is split into two stages - the first takes place here, in Westminster. That's designed to slim the field down to the last two. Once you've got the last two comes the second stage which is where the choice is put to the members. There are around 160,000 members of the Conservative party all over the country, they get to vote by post and have the final say on who they want."
"In the first round of voting here in Westminster you have to have at least eight backers. If you don't have eight you don't make it through the first round. There are other rules, the next round of voting if you don't have enough people you get kicked out. It's all designed to whittle the big long list down to two as quickly as possible."
"The Conservative membership which will get the final say on who the prime minister is are largely thought to be in favor of Brexit, they're thought to be almost in favor of a no-deal Brexit a lot of them, so that means there's a lot of talk about the next prime minister being someone who backed Brexit originally. Theresa May was seen as a 'remainer' and she was never forgiven by some in her party for voting against Brexit, so the view is the next prime minister has to be someone who backed Brexit so they don't run into the same problems that Theresa May did."
At the end of the process in late July, Theresa May's time at 10 Downing Street officially comes to an end.
Until then she'll act as the country's caretaker prime minister.