The European Union proposed on Wednesday that, unless other solutions are found, Northern Ireland will remain in a customs union with the European Union and, for all intents and purposes, the single market as well, when Britain leaves the bloc.

The purpose, as outlined in a draft document, is to ensure that there will be no “hard border” between Ireland and Northern Ireland after the British withdrawal, known as Brexit. That drew a rebuke from Prime Minister Theresa May, who rejected the idea out of hand.

Here is a guide to why this issue is seemingly so intractable, and how it might be settled or otherwise dealt with.

Why Is the Border Such a Big Deal?

The 500-kilometer border between Ireland, which will remain in the European Union, and Northern Ireland, which as part of the United Kingdom will be leaving the bloc, is probably the toughest challenge in talks over Britain’s departure.