1

There are flights from Reykjavik to a few airports in Greenland.

http://en.wikipedia.org/wiki/List_of_airports_in_Greenland

2

This summer there'll be some direct flights from Canada. More info here.

For flights from Iceland to Greenland, take a look at Air Iceland. They serve several destinations in Greenland. Air Greenland has also some flights from Greenland to Iceland.

3

..and apart from Air Greenland and Air Iceland (most routes are only in summer) and cruises - no other "public" transportation in/out of the country.

Difference (slightly simplified) : Air Greenland guarantees connections (i.e. pay for good hotel, food and new tickets) for any delays of flights - ON THEIR OWN planes - i.e. Flying Nuuk-Kangerlussuaq-Copenhagen and fog in Nuuk that delays you 24 hours - will costs you nothing (and they may even try to put in extra flights ) - but you have a problem if you end up missing a plane in Copenhagen.

Air Iceland does not guarantee anything - do not pay for hotel or food if delayed due to weather etc.

These countries are NOT EU-members and travelling in the Arctic is NOT like everywhere else due to weather - so it is the way it is to keep prices from exploding.

4

Those are the only options.