A radial vane rotary engine comprises an outer housing having a inner cam surface, and an inner housing disposed within the outer housing and having a outer cam surface. There is a substantially constant radial distance between the inner and outer cam surfaces. A rotatable rotor is disposed between the inner and outer housings. The rotor is generally cylindrical having an outer surface, an inner surface, a plurality of axial slots opening between the outer and inner surfaces, and an output shaft extending axially from an end portion of the rotor. A plurality of vanes extend radially through the slots between the inner and outer cam surfaces, providing a plurality of outer chambers between the adjacent vanes, the inner cam surface and the outer surface of the rotor. Similarly, a plurality of inner chambers are provided between the adjacent vanes, the inner cam surface and the inner surface of the rotor. The inner and outer cam surfaces are shaped to produce intake, compression, expansion and exhaust states within the inner and outer chambers during a single rotation of the output shaft. The radial vane rotary engine can be adapted to provide bottoming cycle operation to increase fuel efficiency of conventional engines, heat pump operation to replace environmentally damaging refrigerants, air compressor and/or expander operation, and turbocharger operation to increase engine efficiency and power.