Due to the excellent electrical conductivity, superconducting materials are playing an increasingly important role in high-field applications. Lots of superconducting applications rely on the electromagnetic interaction between the permanent magnet (PM) and superconductors in different forms of tapes, bulks and coils. Recently, an electromagnetic interaction between the closed superconducting coil (SC) and the moving PM has been researched with interest. This electromagnetic interaction can both induce and utilize the current in the closed SC, thus achieving the mutual conversion between mechanical and electromagnetic energy wirelessly. In this review, all recently published works about this electromagnetic interaction have been summarised, from aspects of interaction behaviors, mechanism, numerical models, key influence factors and applications. These studies have laid a solid foundation for the follow-up researches.