Organized around expandable space habitat technology, licensed from NASA after the space agency abandoned development of the Transhab project for an expandable space habitat for International Space Station. Ultimately, the company ended up launching some experimental iterations of their implementation of the technology in the early 2000s before constructing a demonstration module that still remains attached to and in use on the International Space Station. Development of several larger modules began, and had entered advanced stages in one case, prior to the company wrapping-up operations. While technically not dissolved, the Bigelow Aerospace is considered no longer in business.
It's important to note that the technology involved is not "inflatable". While soft-walled, the technology involves mechanically-expanding the structures, not blowing them up like a ballon. The benefit of this technology is that a smaller unit can be launched on a rocket, before being expanded in orbit to a size that would otherwise be too large to launch in the form of a traditional fully-assembled module.