This article introduces the basic principle of chirped pulse amplification (CPA) for high-power femtosecond fiber laser amplifiers, along with a discussion of the development status and bottlenecks of the key stretchers and compressors in the CPA structure. It provides a description of the structure and working principle of a typical large-mode-area fiber, and briefly discusses the development status of the corresponding CPA system based on this kind of fiber. Further, it introduces the nonlinear amplification technologies, and discusses an amplification scheme for narrower pulse duration and higher pulse quality. Finally, it presents an analysis of advanced technologies such as an all-fiber structure, coherent beam combination, single-crystal fibers as active elements, and picosecond seed sources, and provides a summary of the development trend of high-power femtosecond fiber laser amplifiers.