Let's meet the two women vying for the nation's top job.
"Brexit means Brexit," Theresa May said when she kicked off her campaign to become the second female British prime minister after Margaret Thatcher.
May is a serious, no-nonsense politician: If she says Brexit means Brexit, it probably does.
She said she was the one to unite the country and lead it forward after Prime Minister David Cameron announced his resignation when his pro-European Union side lost the referendum on whether to remain in the European Union.
"My pitch is simple: I'm Theresa May, and I think I'm the best person to be prime minister," she said.
May had campaigned to remain in the EU, but not loudly, and she is known for her Euroskeptic views.
She ruled out a second referendum, as well as a general election before 2020. She also said that under her leadership, Britain would not apply to leave the E.U. before the end of the year.
She has sought to paint herself as a serious and experienced politician who can unite a divided Conservative Party and a divided country.
"I'm not a showy politician. I don't tour the television studios. I don't gossip over lunch. I don't drink in Parliament's bars. I don't wear my heart on my sleeve. I just get on with the job in front of me," she has said.
May is Britain's long-serving home secretary, a portfolio under which she oversees the vexing issue of immigration. She is praised by some in her party for taking a tough stance on immigration and for introducing visa restrictions on non-EU immigrants in an attempt to drive down net migration. For instance, as of April, Americans and other non-Europeans living in Britain for more than five years have to earn £35,000, or about $47,000, if they want to stay.
She is also reviled by some on the left. Her critics were outraged over a speech she gave last year to the Conservative Party in which she suggested that immigration makes Britain a less cohesive society.
"When immigration is too high, when the pace of change is too fast, it's impossible to build a cohesive society," she said.
Her critics have accused her of using EU nationals as "bargaining chips" in the talks to come with the European Union. She has implied that it would be wrong to give guarantees without getting similar ones for Britons living in the EU.
She once famously said that many voters saw the Conservative Party as the "nasty party." When she launched her leadership bid, she praised Cameron for helping to detoxify the image of the party.
But while she was mostly full of praise for Cameron, she did say that she wouldn't sign up for the current government's plan to turn the budget deficit into a surplus by 2020. She said it was "vital" to continue along a similar path, but she added, "We should no longer seek to produce a budget surplus by the end of the Parliament."
The 59-year-old is the daughter of a Church of England clergyman and says that public service is "part of who I am."
Andrea Leadsom has "the zap, the drive and the determination" needed to be the next prime minister, according to the former London mayor Boris Johnson, who is backing her bid to become the next prime minister.
Leadsom, 53, is an energy minister and a relative unknown in British politics. But on Thursday she beat Michael Gove - Britain's justice secretary, who was widely accused of stabbing Johnson in the back - to become one of two women on the final ballot.
Unlike May, Leadsom campaigned to leave the European Union, and she is running as the candidate who will fully deliver Brexit.
She has said she would move quickly to trigger Article 50 of the Lisbon Treaty, the mechanism by which countries can leave the European Union. She has also said that EU nationals should not be used as "bargaining chips" and should be allowed to stay in Britain post-Brexit.
A former bank executive, she dismissed accusations that she exaggerated her résumé.
Her supporters marched outside Westminster on Thursday chanting, "Leadsom for leader"
But she is the underdog in the race, with May decisively winning the first two rounds of balloting.
Amber Rudd, Britain's energy secretary and Leadsom's boss, told the BBC that the country needs someone who has "real experience" at the top of government. She is backing May.
