geenland or groenland belonged to denmark and norway since 1721, when settlers came there. the treaty of Kiel in 1814 gave its control to denmark after sweden's domination on norway.
later on, norway claimed part of it on 1931 by sending settlers in some parts of eastern groenland, but finally denmark and norway agreed to resolve the problem at the permanent court of international justice on 1933 by giving total contral to denmark.
Greenland rules itself through its parliament, but the head of state is the Queen of Denmark. The position therefore is similar to that of Canada and Australia, which still have the British Queen as Head of State. It is not a member of the EU, although Denmark is.