Abstract: Ultra-large flexible membrane structures are a new type of space structures, which can meet the requirement of some spacemissions. The ability of the flexible membrane in resisting compression stresses is very limited, thus, these structures are often partially wrinkled in their working state on orbit. Wrinkling can change the structuralmechanical performance and affect the structural shape of the surface. Abetter understanding of the effects of wrinkles on structural performanceis important. In this paper,the advances of the study on wrinkles of space membrane structures arereviewed. We mainly discuss the theoretial studies and some related problems. We also point out thedirection of the future studies on wrinkling.