Structural robustness is of great significance to hazard mitigation and risk control. Considerable attempts have been made in this field through the last few decades; however, valid methods of robustness analysis remain unreached. The present paper first reviews and discusses the critical issues concerning robustness analysis, in which the emphasis is placed on the essentials of the conception of robustness, the relationship between a structure and its surroundings (i.e. structure environment interaction), and robustness evaluation. It is argued herein that structural robustness highlights locally damaged states and, therefore, it does not directly reflect the load-bearing capacity, stiffness, redundancy, or reliability of a structure in its pristine/pre-damaged state. Moreover, it shows that besides time-variant effects covered by customary analysis envelope, robustness analysis should consider the time-variant effect of structural form itself, and the conversion of the role of certain components which may arise during failure propagation. Finally, the application of structural robustness in hazard mitigation, especially in multi-hazard mitigation, is stressed.