The main purpose of the old whaling industry, as you can read about it in Moby Dick, was to get whale blubber to render into lamp oil. Whale oil was better than any other illumination-fuel available at the time. It was rendered obsolete, and the industry mostly killed off, by the introduction of petroleum-derived kerosene, and gaslight, and, much later, electric light.
There is still some whaling, especially in Japan, but, as I understand it, nowadays the purpose is to get whale meat, not blubber. Does anybody anywhere hunt for blubber any more?
The Inuit in Alaska still take whales every year. The blubber, or muktuk is considered a treat. While the oil is typically not needed any longer, the traditions are kept alive. Of course, you’re probably asking about commercial enterprise.
According to this site (the reliability of which I cannot vouch for, although they cite wdcs.org), whale oil is still in use for some cosmetics and pharmaceuticals