In the wake of the UK's vote in favour of leaving the European Union (EU), the country will have to contend with the prospect of its Northern Ireland territory sharing a land border with EU member Republic of Ireland, a crossing which currently enjoys a freedom of movement.
"We've had a common travel area between the UK and the Republic of Ireland many years before either country was a member of the European Union. Nobody wants to return to the borders of the past. What we do want to do is to find a way through this that is going to work and deliver a practical solution for everybody," May said after talks with First Minister Arlene Foster and Deputy First Minister Martin McGuinness in Belfast.
Repeating her stance on the EU referendum last month with "Brexit means Brexit but we will be making a success of it", she said, "I'm clear that the Northern Ireland Executive and the other devolved governments will be involved in our discussions as we set forward the UK position."
Her first journey to Belfast as Prime Minister since taking over from David Cameron 12 days ago, follows similar meetings in Scotland and Wales.