Electrodynamically stabilized levitation for high speed rotors is now reaching the borderline between academic interest and industrial application. Prior results of research on electrodynamic bearings (EDB) for high speed rotors have pointed out their unique characteristic of producing positive stiffness by passive means. Among the most interesting features of electrodynamic bearings is the possibility of obtaining stable levitation using standard conductive materials at room temperature and in absence of control systems, power electronics and sensors. Since stable levitation can be achieved by passive means, electrodynamic bearings are an advantageous alternative to active magnetic suspensions: they are less complex, less subject to failure, and cheaper. Although the working principle of EDBs may seem straightforward, the design of a radial suspension relying exclusively on electrodynamic bearings is a challenging task. The topics ralated to the stability of magetic suspensions based on electrodynamic bearings, their modeling and design represent the focus of the present work.