A critical review of methods for critical excitation (worst-case input) is presented to enhance the robustness of structural design of aerospace, mechanical, and civil engineering structures. These structures are often subjected to disturbances including inherent uncertainties due mainly to their occurrence scarcity and worst-case analysis is expected to play an important role in avoiding difficulties induced by such uncertainties. During the last three decades, various critical excitation methods have been proposed extensively and applied to some structural design problems, mainly for important structures of which the failure or collapse must be absolutely avoided. Comparison of the critical responses with the corresponding structural responses to recorded ground motions, deterministic or stochastic treatment, elastic or elastic-plastic responses, system-dependent critical excitations are major subjects of discussion.