But the meeting could be overshadowed over US President Donald's Trumps new immigration controls.
This is Theresa May's first visit to Dublin since she became British Prime Minister and follows on from Enda Kenny's meeting with Theresa May in Downing Street last year.
They've spoken in recent weeks on the phone to discuss the crisis in Northern Ireland and that issue will be up for discussion today.
It's the first meeting between the two since Mrs May outlined her intentions to opt for a hard Brexit.
And so the main focus of their talks will be how they can maintain the common travel area and no return to a hard border between North and South with the UK outside the single market, customs union and curbing immigration.
But after a weekend where Donald Trump initiated a new immigration policy which will be an effective ban on Muslims, both leaders know that could be the only topic of questioning from reporters when they face the media this evening.
Meanwhile the Minister for Children and Youth Affairs Katherine Zappone is hosting discussions today with children and campaigners on the impact of BREXIT on young people.
The Children's Rights Alliance says one of the major concerns is the rate of child poverty.
Chief Executive Tanya Ward says 25 per cent of children in the North and 12 per cent of children in the Republic are living in consistent poverty.
