The frightening looking engine in the video above, which ends up glowing white hot, is a pulsejet. Pulsejets have very few moving parts. They work by compressing the fuel in the combustion chamber by forcing air in. The fuel is then ignited and as it is exhausted it creates a vacuum which draws in and compresses more fuel and air, as well drawing back some of the hot exhaust. The hot exhaust then triggers further combustion. The result is a pulsing of the exhaust gas which give the engine its name.
A clearer explanation, with diagrams, can be found at Bruce Simpson's How Pulsejets Work page at his website. His website has a wealth of information and is well worth a visit. He has numerous projects he describes, including a pulsejet-powered dragster which he describes as being "terrifying" (I believe that), sells kits, books and in has a lot of general information about the engines.
By the way, the video is not Bruce Simpson. It's from another fellow who's home-brewing a pulse jet.