Boris Johnson and Jeremy Hunt face a series of hurdles in the race to Number 10 over the coming weeks.
Here are some of the key events:
June 22
The first hustings for members, organised by Conservative Campaign Headquarters, will take place in Birmingham, hosted by broadcaster Iain Dale.
Mr Johnson and Mr Hunt will each make a short pitch to the audience, followed by questions from Dale and the Tory members at the event.
June 26
A “digital hustings” has been organised by Conservative Campaign Headquarters (CCHQ) as part of the contest.
June 27
The second hustings for Tory members will take place in southern England. CCHQ has organised a total of 16 hustings and there have been more than 20,000 applications to attend.
June 28
Hustings in south-west England.
June 29
Two hustings – in the Lakes and Borders region and north-west England.
July 4
Hustings in the Yorkshire and Humber region.
July 5
Two hustings, in north-east England and Scotland.
July 6
Two hustings, in the East Midlands and Wales.
July 6-8
Conservative members should receive their postal ballots.
July 9
Mr Hunt and Mr Johnson will go head-to-head in an ITV debate hosted by Julie Etchingham.
The BBC and Sky News also want to hold TV specials involving the two leadership hopefuls.
July 11
Hustings in south-east England.
July 12
Hustings in Gloucestershire.
July 13
Two hustings, in Cambridgeshire and Essex.
July 17
The final hustings will take place in London.
Week commencing July 22
A new leader will be announced following the ballot of 160,000 Conservative members.
Prime Minister Theresa May will then see the Queen to formally resign and the new leader will be invited to Buckingham Palace to form a government.