It's your typical 'special squad' crime drama, with the twist that each episode is loosely based on a story from an old Greek epic poem called the Odyssey. This is kind of laboured sometimes, with hilarious panto results. The script writers have thought up all sorts of elaborate ways of preventing Halgrim from getting to his rural Icelandic home, because Halgrim is (of course) Odysseus, after whom The Odyssey is named, and the storyline of The Odyssey is one mishap after another that prevents Odysseus getting home from a long sea voyage. In case this wasn't enough ancient symbolism, they've thrown a bunch of Bible references in too. So Halgrim is Jesus, as well as Odysseus. Also, his nickname is from a Danish folk tale, and he is the best cop in the special squad. In other words, he is a super mythically charged, super religiously charged, international crime fighting super cop. And he has the personality to match such an uber alpha mission, complete with retarded social skills and dysfunctional relationships with (many) women.
At some stage during the series, Nazim (the token Arab - in true token style, he is the first one of the cast to get killed) - Halgrim's colleague from their UN peace keeping army days (of course) - describes how he got his nickname. It is because 'he flies above us, seeing it all.' which I guess is a nice way of saying he keeps all the information to himself, doesn't trust his colleagues and works all the time to avoid his personal problems.
Halgrim is likable in an arch villain presented as hero kind of way. Apart from Halgrim, the show is very good. The action is interspersed with flyover views of beautiful, rugged countryside, gritty-but-beautiful shots of Copenhagen, Stockholm and a smattering of other European cities. And every now and then, the special squad and their international crime fighting colleagues have teleconferences where they all speak English in their cute Euro accents. Just what the export market loves.