High power Yb-doped fiber lasers have gained increasing application in space environment. However, the space radiation will bring color centers in Yb-doped fiber materials, thus increasing the inherent loss of the fiber. As a result, the optical properties of typical fiber-based components and the fiber lasers will be deteriorated, which makes it difficult for high power fiber lasers to achieve long-term stable operation in space environment. In this paper, a detailed introduction from three main aspects is given. Firstly, the influence of space radiation on typical optical components, thermal loading and nonlinear effects in high power fiber laser are introduced. Next, the typical suppressing methods of space radiation and their feasibility in high power fiber laser system are discussed. In the end, the representative research progress on the influence of space radiation on high power Yb-doped fiber lasers and effective suppressing methods at home and abroad are introduced.