Abstract
In contrast to the interaction between two magnets with opposite magnetization directions, the interaction between a permanent magnet and a superconductor can be stable and result in magnetic levitation. This property can be exploited for the development of high velocity rotating bearings with no mechanical contacts and for the development of levitated trains. In this review, we focus on this latter application. After a brief description of the other techniques developed for levitating trains and the resulting achievements, we describe the magnet-superconductor interaction and recall the achievements in this field. We then give insights into the properties of the employed magnets and arrangement of magnets and we detail the characteristics and the fabrication processes of the most frequently used superconductors. Focusing on physics, we detail the procedures generally used for measuring the vertical (levitation) and the lateral (guidance) forces in magnetic levitation and the results obtained from experiments. We detail and give a critical review of the various models proposed for reproducing the force measurements. In the conclusion we discuss the possible future developments of the technology.