Typically they're now using diesel engines, or Jet-A. Some are using gas. However, you can use almost any fuel. In fact, the old Zeppelins used a mixture of methane and hydrogen, which was very environmentally benign 75 years ago.
The advantage of an airship is that it's so big, you can have a very large low-pressure tank. You can use a gaseous fuel like hydrogen or methane without having to compress it and getting a heavy tank inside. They do have lots of options.
Stu, would you like to comment on this?