Conservative MPs will vote between 18:00 GMT and 20:00 GMT.
The challenge to Mrs May's position comes after the required 48 letters calling for a contest were delivered. Mrs May, who has been prime minister since shortly after the UK voted to leave the European Union in 2016, has faced criticism in her party for the Brexit plan she has negotiated.
It is not yet known how quickly the result of the vote will be announced, but Mrs May needs to get a majority in her favour to win it. If that happens she cannot be challenged for at least another year.
If Mrs May does not win the vote there would then be a Conservative leadership contest in which she could not stand. There is also an option that even if Mrs May won - but not overwhelmingly - she may decide to stand down as party leader.
As the Conservative Party is the largest party in the House of Commons, whoever is leader of the party would be expected to be prime minister.
If Mrs May is ousted as Conservative leader later she would be expected to stay on as a caretaker prime minister until a new leader is selected by the party, a process that could take six weeks.
If there are multiple candidates, Conservative MPs hold a series of votes to choose two to go forward to a vote of party members.
13:30 – USD: CPI MoM; Forecast 0.0% against previous of 0.3%
13:30 - USD: Core CPI MoM; Forecast same as previous at 0.2%
All Day - GBP: No Confidence Vote Developments