It's extremely difficult to resolve due to the tangled history tying Northern Ireland to the United Kingdom despite its cultural and geographic ties to the Irish republic. Brexit forces the issue because once Britain leaves the bloc, the border between Ireland and Northern Ireland will be the only land border between the EU and the U.K.
The border has been open and unguarded for 20 years since the Good Friday agreement ended the armed conflict in Northern Ireland, but that status will be much more difficult to maintain once Britain is no longer part of the EU. A host of new trade rules and tariffs are likely to apply, along with possible vehicle checks.
That could mean a "hard border" is put in place, potentially reigniting old passions and leading to violence.
Colm Barton of Londonderry, Northern Ireland, said Tuesday the changes Brexit would bring have "the potential to destroy" the peace process that ended decades of violence known as "The Troubles." A hard border is unacceptable, he said.
"No matter what we dress it up as, it will ultimately end with (the) British army protecting British installations on the island of Ireland, and it is absolutely insane," he said.
Other residents simply detest the hassles a hard border would bring.
"That means it's going to be back to the old days," said Seanna Happsley, who crosses the border daily for her commute. "Back to the way it was before. Just practical things, school, going to work every day, taking the kids to school and so on, that is going to take a lot of time and so on."
The so-called backstop that is part of the U.K.'s withdrawal agreement from the EU is designed to ensure there is no hard border — no customs checks or other border structures — after Britain withdraws from the bloc. It says if no other solution is found, Britain will remain in a customs union with the EU in order to keep the Irish border open.
Brexit supporters fear that the backstop could last indefinitely, tying Britain to the EU even after it formally left — in effect, defeating one of the main purposes of leaving in the first place.
One possible solution would be for Northern Ireland to stay in a customs union with the EU while Britain departs, but British leaders have categorically ruled this out because it would effectively place a border in the Irish Sea between Northern Ireland and the British mainland.
Some officials believe a technological solution may eventually make physical border checks unnecessary. For now, the backstop remains a considerable obstacle to a divorce deal.
Katz reported from London.