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Terahertz band in electromagnetic spectrum has many properties than traditional light source, which has very important research value in biology, material, security, communication and other fields. The high power and high efficiency terahertz radiation source is an important factor and prerequisite for the transformation of terahertz technology into actual productivity. In this paper, the research progress of terahertz wave generated by laser interacting with different excitation media is summarized from the perspective of gas, solid and liquid as excitation media. The physical mechanism of four-wave mixing, mass-dynamic, cherenkov and photocurrent models commonly used in gas media, as well as the physical mechanism of photo-conductance and photorectification models in solid media are described in detail, and the factors affecting the generation of terahertz waves by these excitation media are analyzed and summarized. Finally, the methods of producing terahertz radiation source by liquid excited medium are prospected.