This paper is about hybrid reluctance machines, in which the stator or fixed part has a combination of U-shaped electromagnets with permanents magnets placedbetween their arms while the moving part is simply a structure with salient poles. They can be designed to build different types of rotary or linear electric motors and generators with outstanding performances. In this paper, first, the principle of operation of these machines is explained. Then different types of hybrid reluctance machines using this particular structural configuration are described showing their potential based on simulations and experimental results.