Iceland is not a member-state in the EU but they have close economic and political ties. They are a part of the European Economic Area (EEA) and the European Free Trade Association (EFTA).
They once applied for membership after the financial crisis but it didn't go through; currently most citizens are opposed to the idea.
Becoming a full EU member would require them to accept the EU's fishing limitations, potentially hurting their economy. There are also other factors involved:
https://en.wikipedia.org/wiki/Iceland%E2%80%93European_Union...
