Here is a very interesting article about greenland sharks: http://www.spiegel.de/wissenschaft/natur/0,1518,473863,00.html
As it is in german, most of you will probably not understand it. I´ll try to put the content in a nutshell: Greenland sharks are no sluggish deep sea scavengers. Recent studies showed that their diet consists to a big part of seals, and it is very unprobable that they were all already dead when they were eaten by the sharks. They have also often salmons in their stomaches, which are also very fast fish. Furthermore studies with transmitter-marked sharks showed that they swim not only in deep water, but also very often in minimal depths, often directly under the ice, most probably to hunt for seals. If they are really such active and efficient predators, it could really be that they actually hunt living giant and colossal squid.
What is also facinating is their incredibly slow growth rate, potentially the larger specimens are well over a hundred years old ("hundreds of years theoretically" according to the article, putting stress on the adjective). Bowheads spring to mind.