The growing acceptance of the concept of variability in the properties of structural materials (fracture toughness of metals, differences in composite fibers, etc.), along with the inherent randomness of loading due to nature, has caused the approach of analyzing structural systems using reliability techniques to become increasingly important. Classical reliability analysis is traced from basic probability theory to the development of fiber bundle theory with its resulting features and limitations. Recent applications of reliability analysis to “weak-link” structural systems are cited. Current research in the probabilistic treatment of physically redundant structures is then discussed with emphasis on the proper definition of convolution integral limits and the problems involved in the statistical modeling of real engineering components. Recent and anticipated trends in the application of reliability techniques to analyzing redundant structures are examined, including risk analyses of current Air Force aircraft and the “wearout” approach to life expectancy. Conclusions are drawn concerning the role that risk analysis could play in modern aerospace design and in establishing structural design criteria.