Distinct from the conventional machines with only one electrical and one mechanical port, electrical machines featuring multiple electrical/mechanical ports (the so-called multi-port electrical machines) provide a compact, flexible, and highly-efficient manner to convert and/or transfer energies among different ports. This paper attempts to make a comprehensive overview of existing multi-port topologies, from fundamental characteristics to advanced modeling, analysis, and control, with particular emphasis on the extensively investigated brushless doubly-fed machines for highly-reliable wind turbines and power split devices for hybrid electric vehicles. A qualitative review approach is mainly adopted but strong efforts are also made to quantitatively highlight the electromagnetic and control performance. Research challenges are identified and future trends are discussed.