Due to its exceptional advantages, such as high specific strength, high specific modulus, and good fatigue resistance, carbon-fiber-reinforced plastic (CFRP) is frequently utilized in aerospace, aviation, automotive, rail transportation, and other areas. Composite components typically need to be joined and integrated. In the equipment manufacturing industry, the most used methods for processing composite components are cutting, drilling, and surface treatment. The quality of CFRP is significantly impacted by traditional mechanical processing, causing flaws like delamination, burrs, and tears. Laser processing technology has emerged as a crucial method for processing CFRP for its high quality, non-contact, simple control, and automation features. The most recent research on the laser processing of CFRP is presented in this paper, supporting scientists and engineers who work in the field in using this unconventional manufacturing technique. This paper gives a general overview of the key features of laser processing technology and the numerous machining techniques available. The concepts and benefits of laser processing technology are discussed in terms of the material properties, mode of operation, and laser characteristics, as well as the methods to achieve high efficiency, low damage, and high precision. This paper reviews the research development of laser processing of carbon-fiber-reinforced plastics, and a summary of the factors affecting the quality of CFRP laser processing. Therefore, the research content of this article can be used as a theoretical basis for reducing thermal damage and improving the processing quality of laser-processed composite materials, while, on this basis, we analyze the development trend of CFRP laser processing technology.