A survey of linear-motion electrical machines is presented. Although various types of dc and ac linear machines are briefly mentioned, linear induction motors are the main concern of the paper and they are discussed in considerable detail. Based on topological considerations, a classification of these machines is presented and their development through the last 70 years is reviewed. A brief qualitative description of the newly developed hybrid machine is also included. Analysis and design problems, and some solutions, as unique to linear machines are discussed. Several possible applications of these machines are included.