A comprehensive approach has been achieved for conducting failure detection, identification, and prognostics of systems, subsystems, and components in health-monitoring applications and as part of condition-based maintenance systems. A compound method composed of optimal filtering, statistical analysis, and fuzzy Adaptive Resonance Theory based Mapping networks is able to detect and diagnose system and sensor/actuator failures. Although previously proven in the literature to be successful for systems that are well-described in a state-space representation, current research has shown the viability in extending the scheme to unknown and nonlinear systems while stillmaintaining failure detection and identification capabilities. This utility of themethod has been demonstrated in a case study for determining failures in a known reusable liquid rocket engine model and an unknown input-output relation in a fluid flow test bed. Then, for providing prognostic statements regarding the remaining life of a component, research has also focused on an integrated neuro-fuzzy system. The developed technique uses fuzzy logic and rule-based knowledge for the preprocessing of training data, which is then fed into an artificial neural network for learning. Once trained, the artificial neural network was tested and deployed for prognostics by estimating remaining useful life.