I seriously doubt that no more than a handful of people have even heard of a rotary engine…but its really awesome, so continue reading 
There are different types of rotary engines. They can be piston engines or pistonless (Wankel Engines come in pistonless, which will be covered in a later post ;p)
The rotary engine was an early type of internal-combustion engine, usually designed with an odd (usually either 7 or 9, so that a consistent every-other-piston firing order could be maintained, to provide smooth running) number of cylinders in a radial configuration, in which the crankshaft remained stationary and the entire cylinder block rotated around it, unlike normal engines where the crankshaft rotates. Its main application was in aviation.

This type of engine was widely used as an alternative to conventional inline engines (straightor V) during World War. By the early 1920s, however, the inherent limitations of this type of engine had rendered it obsolete, i.e the weight and air resistance along with inefficient use of fuel and lubricating oil. These caused problems for inexperienced pilots.

Three key factors contributed to the rotary engines success at the time…

1. Smooth running: Rotaries delivered power very smoothly because there are no reciprocating parts, and the relatively large rotating mass of the cylinders acted as a flywheel.
2. Weight advantage: many conventional engines had to have heavy flywheels added to smooth out power impulses and reduce vibration. Rotary engines gained a substantial power-to-weight-ratio advantage by having no need for an added flywheel.
3. Improved cooling: when the engine was running the rotating cylinder block created its own fast-moving cooling airflow, even with the aircraft at rest.

The favourable power-to-weight ratio of the rotaries was their greatest advantage during the WWI. While larger, heavier aircraft relied almost exclusively on conventional in-line engines, many fighter aircraft designers preferred rotaries right up to the end of the war.

But by the time the war ended, the rotary engine had become obsolete, and it disappeared from use quite quickly due to their high fuel consumption and high air resistance( air drag increases with the square of velocity).

Now-a-days if you say rotary engine, people begin to think of the ‘wankel engine’ which was a poistonless rotary.(we will cover it in a future post  )