Linear electromagnetic motors (LEMs) have been proposed, developed and used to propel high-speed (i.e. speed > 100 m/s) levitating vehicles. However, few real implementations have demonstrated the feasibility of these machines at such speeds. Furthermore, LEMs are expected to be enabling technologies for levitating vehicles traveling at near sonic speed, such as the Hyperloop concept. This paper presents a systematic review of modeling, design and performance assessment of LEMs used (or proposed) for the propulsion of levitating high-speed vehicles. Among all the possibilities, those that have received the most attention since the 1960s, along with the first magnetic levitation train concepts, are discussed. Classified by operating principle and topology, the LEMs are compared in terms of design and performance via specific key performance indicators. The performance of the various proposed LEMs is assessed on the basis of data available in the literature.