Composites reinforced with woven or braided textiles exhibit high structural stability and excellent damage tolerance thanks to yarn interlacing. With their high stiffness-to-weight and strength-to-weight ratios, braided composites are attractive for aerospace and automotive components as well as sports protective equipment. In these potential applications, components are typically subjected to multi-directional static, impact and fatigue loadings. To enhance material analysis and design for such applications, understanding mechanical behaviour of braided composites and development of predictive capabilities becomes crucial. Significant progress has been made in recent years in development of new modelling techniques allowing elucidation of static and dynamic responses of braided composites. However, because of their unique interlacing geometric structure and complicated failure modes, prediction of damage initiation and its evolution in components is still a challenge. Therefore, a comprehensive literature analysis is presented in this work focused on a review of the state-of-the-art progressive damage analysis of braided composites with finite-element simulations. Recently models employed in the studies on mechanical behaviour, impact response and fatigue analyses of braided composites are presented systematically. This review highlights the importance, advantages and limitations of as-applied failure criteria and damage evolution laws for yarns and composite unit cells. In addition, this work provides a good reference for future research on FE simulations of braided composites.