**Abstract**

Terahertz electromagnetic wave is one of the hottest research topics in nowadays scientific world thanks to its broad applications in material characterization, medical imaging, wireless communication, and security checking etc. Using free-electron beams to interact with periodic structures via the famous Smith-Purcell effect is an efficient way of generating high-power terahertz radiation. In this chapter, we introduce the basic theory and latest developments of the terahertz radiation schemes using a free-electron beam (including continuous electron beam, a single electron bunch, and a train of electron bunches, etc.) to interact with periodic electromagnetic structures, including grating, surface plasmonics, and subwavelength hole arrays, via a special Smith-Purcell effect or Cherenkov-like effect. A kind of free-electron lasers based on the special Smith-Purcell radiation in the terahertz region is proposed and investigated, which can be developed as high-power terahertz wave sources for practical applications.

**Keywords:** Terahertz, free-electron beam, beam-wave interaction, diffraction radiation
