There is no longer any subsistence hunting of whales in the lower 48 - all remaining subsistence harvest in the US takes place in Alaskan waters. The Makah would be the lone exception if they are again granted the right to hunt.
The bowhead whale hunt in the Beaufort and Chukchi Seas is the most well known subsistence hunt. The Beuafort Sea population of Bowheads is around 10-12,000 animals and increasing at about 3% per year. The Inupiats have undertaken decades of efforts to document population levels. The Int'l Whaling Comm'n allots them 50-60 whales/year, which are divided between the Spring and Fall hunt. The bowhead hunt is widely consisdered to be sustainable and well managed. Alaskan Natives also regularly hunt beluga whales - I don't know much about the hunt of other species.
In the spring the Inupiats hunt from seal skin boats, powered by oars and use hand propelled harpoons with explosive tips. In the fall, the conditions in the Arctic Ocean force them to use 15-20' open cockpit aluminum boats with a single outboard motor.
Whale meat makes up a huge portion of their annual diet, and the studies document dramatically increased health risks from conditions such as diabetes when Inupiats change from a subsistence diet.
If you're interested, we've got up some information on offshore oil and threats to the subsistence hunt. You'll find some maps of the subsistence hunting grounds, pictures of the boats and a description of the whaling techiniques and information on threats posed to the subsistence hunt.