Mr Sunak and Ms Truss are now taking part in nationwide leadership hustings events, with their next appearance happening on 16 August in Perth.
This is the only hustings event taking place in Scotland.
Tory party members will then vote on their favourite candidate, with the winner - and therefore the UK’s next prime minister - announced on 5 September.
But what are hustings, who can attend, when are they taking place, and how can I watch them?
Here’s everything you need to know.
What are hustings?
According to the Oxford Dictionary, ‘hustings’ are the “political meetings, speeches, etc. that take place in the period before an election”.
Similarly, the Electoral Commission defines the term as “a meeting where election candidates or parties debate policies and answer questions from the audience”.
Voters are able to hear the views of the parties - or in this case, the candidates - and ask questions on the key issues.
The idea is these events enable voters to make a more informed decision.
Who can attend?
Only eligible voting members of the Conservative Party can attend the hustings in person.
If you are eligible, you will need to register for a ticket - which costs £5.
Those who are unable to attend in person can register online for virtual hustings streams.
When are they taking place?
Below is the timetable for the upcoming hustings, as listed on the Conservative Party’s website.
The next hustings event will see Mr Sunak and Ms Truss go head-to-head in front of a live audience in Perth on 16 August.
What are the leadership election rules?
Conservative Party leadership elections consist of two stages:
Stage 1: Conservative MPs choose two candidates to put forward to stage two.
This takes place through a series of votes, and is how the field has been narrowed down to Ms Truss and Mr Sunak. Those who were eliminated from the contest during this stage were:
- Penny Mordaunt
- Kemi Badenoch
- Tom Tugendhat
- Suella Braverman
- Jeremy Hunt
- Nadhim Zahawi
Stage 2: The two MPs selected in Stage 1 face a ballot of Conservative Party members.
This is done on the basis of one member, one vote. You must be a member of the Conservative Party to vote.
Ballots will be posted to members, and are due to arrive between 1 August and 5 August. The vote closes at 5pm on 2 September, with the outcome due to be announced on 5 September.
The candidate who receives the most votes wins, and will become the next prime minister.