Continuous fiber reinforced polymer composites (CFRPCs) have been widely used in the aerospace field due to their advantages of lightweight, high specific strength, and high modulus. However, its manufacturing cost has always been high, and the emergence of additive manufacturing technology has opened up new directions for the design and manufacturing of high-performance, low-cost complex composite structures. This study reviews the design changes, material systems, and process progress brought about by the additive manufacturing technology of CFRPCs, and analyzes the performance defects of CFRPCs in extrusion molding additive manufacturing. Further analysis was conducted through relevant literature on the relationship between extrusion molding additive manufacturing process, microstructure, and performance, providing a reference direction for improving the performance of additive manufacturing CFRPCs. Furthermore, this article summarizes the typical applications and future prospects of additive manufacturing of CFRPCs. Composite additive manufacturing will continue to play an important role in the application of composite materials in aerospace field.