Zeppelin: Properly, Zeppelin is a trade name of the company of the same name. However, their brand has become somewhat genericized, and is often used to refer to rigid airships of the kind they pioneered, even if built by someone else. Historically, Zeppelin not only built the two largest airships ever, the hydrogen-filled Hindenberg and Graf Zeppelin II, they also partnered with Goodyear to build the two largest helium-filled airships in history, the USS Macon and USS Akron. All in all, Zeppelin constructed 130 airships, and a successor company, Zeppelin NT is still building airships in the twenty-first century. Fun footnote: the first airline (yes, the first airline ever) was DELAG, and they began passenger service with Zeppelin airships in 1910.
Tech Level: The first powered flight was made in a steam-powered dirigible in 1852, although the vessel could barely cope with a light breeze. Big rigid airships are a staple of Steampunk, although actual Zeppelins, at least the later ones, had diesel engines, so on technical grounds would more accurately fall into Dieselpunk. However, one reason airships are often featured in Steampunk has to do with their individuality. Like ocean liners, airships were one-offs, rather than mass-produced like, say, Boeing airliners. For more on the difference between Steampunk and Dieselpunk, see this blog post by my dieselpunk writing friend, Lindsay Kitson, or this one by Jason Sheehan. With airships, bigger is better: as they grow, their volume (and therefore lifting ability) rises sharply. A very large airship could carry such massive items as steam engines and coal for a long journey, or solar cells and huge batteries to fly at night, so both steampunk and solarpunk are possible.
Appeared In: Brand-name Zeppelins made multiple appearances in Indiana Jones movies. The Golden Compass, and many other Steampunk works, featured rigid airships of similar design.
For Your Plot: Rigid airships have bad history with thunderstorms, and early airships had unheated passenger cabins that were freezing cold due to the altitude. There must be a plot development or two there. Otherwise, airships are a grand way to factor aviation into alternative world-building, and you don’t have to stick with neo-Victorian.