Radial (centrifugal) compressors can be built rather compact and are known to be robust in handling. They find their widespread application in aero-engines of small- and medium power. They serve as turbo-chargers in land-, sea- and airborn reciprocating engines as for example in trucks, tanks, ships and airplanes. They are further used to compress gases in industrial processing engineering and to ventilate air in several household appliances. Within small turboprop aero-engines, radial compressors can replace some axial compressor stages and hence reduce weight and cost. Two-stage radial compressors are able to reach pressure ratios of 20:1for those turbomachines. A 40:1 pressure ratio for large turbofans can be reached with a rear radial stage in the core engine part. Radial compressors are robust and rather cheap to manufacture, since in most cases each stage has only two integral components, the impeller and the diffuser, made from one production part each. The General Aviation Propulsion Program, that has been placed in the U.S. underlines the importance of the aero-thermodynamical reasearch for radial compressors. It aimes at more efficient as well simpler engines for commuter aircrafts. These new machines are expected to become 10 times cheaper than today's engines, even though they will be manufactured by highly developed die-casting and milling machines. The development of unconventional blading and casing is expected to play a key role to more efficient radial compressors.