Mrs May will stay on as prime minister and acting party leader until her replacement is chosen, probably in the week beginning July 22.
The fiercely competitive race to Number 10 has already seen a number of candidates drop by the wayside, as new rules mean contenders must have the backing of eight MPs.
Boris Johnson is the current frontrunner, despite cabinet ministers Amber Rudd and Penny Mordaunt backing Foreign Secretary Jeremy Hunt.
Mark Harper, Andrea Leadsom, and Esther McVey were eliminated in the first round of voting, Matt Hancock dropped out and Dominic Raab did not make the cut in the second round of voting by Tory MPs.
Mr Johnson topped the latest ballot with 126 votes, which puts him over the magic number of 105 that places him, in effect, in the final two.
Currently in the running to be the next prime minister are:
- Boris Johnson
- Jeremy Hunt
- Michael Gove
- Sajid Javid
- Rory Stewart
So, what happens next and when will we know who the new prime minister is?
Wednesday June 19 and Thursday June 20
The pool of candidates will be reduced significantly as more ballots take place on June 19 and 20.
The contender who comes last is eliminated until just two candidates remain on the ballot paper.
If more ballots are needed to whittle the candidates down further, these will take place on Thursday evening or Friday.
Saturday June 22
The final pair of candidates will take part in hustings in front of Conservative Party members.
Members will spend a month deciding on who they want to lead the party and be the next Prime Minister.
The party's 150,000 members will vote by a postal ballot - the final ballot - and the result will be announced in July.
Monday July 22
The result of the membership ballot will be announced the week commencing July 22.
The new Tory leader and the country's new Prime Minister should be in place before the summer parliamentary recess.
Theresa May will visit the Queen to tender her resignation and her successor is expected to be called to Buckingham Palace to form a government.