The earliest attempts at jet engines were hybrid designs, in which an external power source supplied the compression. In this system (called a thermojet by Secondo Campini) the air is first compressed by a fan driven by a conventional gasoline engine, mixed with fuel, and then burned for jet thrust. Three known examples of this type of design were the Henri Coanda's Coanda-1910 aircraft, the much later Campini Caproni CC.2, and the Japanese Tsu-11 engine intended to power Ohka kamikaze planes towards the end of World War II. None were entirely successful, and the CC.2 ended up being slower than a traditional design with the same engine.
The key to the useful jet engine was the gas turbine, used to extract energy to drive the compressor from the engine itself. Work on such a "self-contained" design started in England in 1930 when Frank Whittle submitted patents for such an engine (granted in 1932) using a single turbine stage in the exhaust to drive a centrifugal compressor. In 1935 Hans von Ohain started work on a similar design in Germany, seemingly unaware of Whittle's work.
Ohain approached Ernst Heinkel, one of the larger aircraft industrialists of the day, who immediately saw the promise of the design. Heinkel had recently purchased the Hirth engine company, and Ohain and his master machinist Max Hahn were set up there as a new division of the Hirth company. They had their first HeS 1 engine running by 1937. Unlike Whittle's design, Ohain used hydrogen as fuel, which he credits for the early success. Their subsequent designs culminated in the HeS 3 of 1,100 lb (5 kN), which was fitted to Heinkel's simple He 178 airframe and flew in August 1939, an impressively short time for development. The He 178 was the world's first jetplane.
In England, Whittle had significant problems in finding funding for research, and the Air Ministry largely ignored it while they concentrated on more pressing issues. Using private funds he was able to get a test engine running in 1937, but this was very large and unsuitable for use in an aircraft. By 1939 work had progressed to the point where the engine was starting to look useful, and Whittle's Power Jets Ltd. started receiving Air Ministry money. In 1941 a flyable version of the engine called the W.1, capable of 1000 lb (4 kN) of thrust, was fitted to the Gloster E28/39 airframe, and flew in May 1941.
One problem with both of these early designs, which are called centrifugal-flow engines, was that the compressor works by "throwing" air outward from the intake to the sides of the engine, where the air is then compressed by being "crushed" up against the side. This leads to a very large cross section for the engine, as well as having the air flowing the wrong way after compression - it has to be collected up and "bent" to flow to the rear of the engine where the turbine is located.
German Anselm Franz of Junkers' engine division (Junkers Motoren, or Jumo) addressed this problem with the introduction of the axial-flow compressor. Essentially, this is a turbine in reverse. Air coming in the front of the engine is blown to the rear of the engine by a fan, where it is crushed against a set of non-rotating blades called stators. The process is nowhere near as powerful as the centrifugal compressor, so a number of these pairs of fans and stators are placed in series to get the needed compression. Even with all the added complexity, the resulting engine is much smaller. Jumo was assigned the next engine number, 4, and the result was the Jumo 004 engine. After many teething troubles, mass production of this engine started in 1944 as a powerhouse for the world's first fighter aircraft, the Messerschmitt Me 262. The Me 262 came too late to decisively impact Germany's position in World War II, but it will be remembered as the first use of jet engines in service. After the end of the war, the German Me 262 aircraft were extensively studied by the victorious allies, and contributed to work on early Soviet and US jet fighters.
British engines also were licensed widely in the US. American designs wouldn't come fully into their own until the 1960s. Their most famous design, the Nene, would also power the USSR's jet aircraft after a technology exchange.
There are a number of types of jet engines, all of which are based on the principle that air is compressed and used as an oxidizer for the fuel. Some examples are as follows: