Nonrigid use a little airpressure to retain the ship's shape. The first nonrigid airships were built by the French. In 1852 Henri Giffaud built an airship of 3,200 cubic meters powered by a steam engine. Blimps were effectively used by the British and French in World War I in maritime reconnaisance against German submarines.
In World War II the United States was the only power to use airships. The navy used them for minesweeping and anti-submarine patrols. After 1945 the navy continued to use blimps for anti-submarine warfare and offshore early warning of bomber attacks until 1962.
Since then the Goodyear fleet of blimps has been about the only examples. The first Goodyear blimp was built in 1919, several in the 1930s. So the primary uses for airships are now advertising and a little tourism.