The standard tools of control theory begin with assumed accurate models of a system and provide means for system control to achieve desired objectives. When uncertainty is taken into account, methods are also available for obtaining results that enjoy some robustness properties with respect to the uncertainty. However, today many engineered systems are operating at levels of stress and with degrees of uncertainty that render such techniques to be of marginal value in system operation. In this lecture, several existing approaches to the monitoring the vulnerability of complex uncertain systems under stressed operation are discussed, and new contributions are given. The benefits and limitations of using exogenous probe signals are pointed out. Techniques for determining areas within a system that are of most value in system monitoring are developed, and these techniques are shown to provide a means both for detecting and localizing the vulnerability of the complex system to disturbances and to collapse.