The Faroes are part of Denmark with home rule, the queen of Denmark is the monarch, the Danish Krone in a Faroese guise is the currency, the language is closely related to Icelandic but while Icelandic is essentially Norse, Faroese has developed somewhat away from the origin. The Faroes are not in the EU but they have two bilateral agreements with it, one on free trade the other on fisheries (the latter being why the Faroes stayed outside when Denmark joined). The Faroes also have agreements with EFTA and the other Nordic countries. It is a very small country with a small population.
I have been more than once - a very unusual place and delightfully informal yet organised/focussed, energetic and advanced, in that way not unlike Iceland. Each of the islands is quite small, lots of mountains and cliffs, very little flatland but getting around by car is impressively easy. There are one or two tunnel connections between islands but otherwise it is a case of crossing by boat. The climate is maritime and therefore, given the position, very variable.