The thesis presents a framework for integrating models, simulation, and experimental data to diagnose incipient failure modes and prognosticate the remaining useful life of critical components, with an application to the main transmission of a helicopter. Although the helicopter example is used to illustrate the methodology presented, by appropriately adapting modules, the architecture can be applied to a variety of similar engineering systems. Models of the kind referenced are commonly referred to in the literature as physical or physics-based models. Such models utilize a mathematical description of some of the natural laws that govern system behaviors. The methodology presented considers separately the aspects of diagnosis and prognosis of engineering systems, but a similar generic framework is proposed for both. The methodology is tested and validated through comparison of results to data from experiments carried out on helicopters in operation and a test cell employing a prototypical helicopter gearbox. Two kinds of experiments have been used. The first one retrieved vibration data from several healthy and faulted aircraft transmissions in operation. The second is a seeded-fault damage-progression test providing gearbox vibration data and ground truth data of increasing crack lengths. For both kinds of experiments, vibration data were collected through a number of accelerometers mounted on the frame of the transmission gearbox. The applied architecture consists of modules with such key elements as the modeling of vibration signatures, extraction of descriptive vibratory features, finite element analysis of a gearbox component, and characterization of fracture progression. Contributions of the thesis include: (1) generic model-based fault diagnosis and failure prognosis methodologies, readily applicable to a dynamic large-scale mechanical system; (2) the characterization of the vibration signals of a class of complex rotary systems through model-based techniques; (3) a reverse engineering approach for fault identification using simulated vibration data; (4) the utilization of models of a faulted planetary gear transmission to classify descriptive system parameters either as fault-sensitive or fault-insensitive; and (5) guidelines for the integration of the model-based diagnosis and prognosis architectures into prognostic algorithms aimed at determining the remaining useful life of failing components.