The pure-quartic soliton fiber laser is an innovative ultra-short pulse laser that can maintain a stable pulse shape through a balance between fourth-order dispersion effect and self-phase modulation effect. Comparing with traditional soliton laser that is dominated by second-order dispersion, the mode-locked pulse energy of pure-quartic soliton laser can be 1–2 orders of magnitude higher. This provides researchers with new ideas for developing high-energy and high-peak-power fiber lasers. Here, the generation and transmission characteristics of pure-quartic solitons in nonlinear optical systems such as fiber lasers in recent years are systematically reviewed. It also explores some special transient dynamic phenomena. Furthermore, in this article, the latest achievements of our research group in this area are also presented. Finally, the application prospect and development trend of pure-quartic soliton fiber lasers are prospected. These results will contribute to a more comprehensive understanding of the basic physical properties of pure-quartic soliton fiber lasers.