The UK and the EU have agreed a provisional deal on the border and other issues that will allow work to move on to the second stage of Brexit negotiations.
Here are some of the key quotes from this morning.
European Commission President Jean-Claude Juncker
''I believe we have made the breakthrough we needed. Today's result is, of course, a compromise.''
British Prime Minister Theresa May
''In Northern Ireland, we will guarantee there will be no hard border.''
Taoiseach Leo Varadkar
"Today is a very significant day for everyone on the island of Ireland, for our neighbouring island and for all our fellow members of the European Union."
Tánaiste Simon Coveney
"There is no scenario now in the context of Brexit that will result in a hard border.''
European Council President Donald Tusk
''Breaking up is hard, but breaking up and building new relations is much harder.''
Sinn Féin Deputy Leader Mary Lou McDonald
"Theresa May and the British government have repeatedly very, very clearly that they - and by 'they' they mean us in the North - will leave the customs union and the single market and that presents for us a real and present danger that is highly problematic."