This chapter reviewed generic prognosis algorithmic approaches and introduced some of the basics associated with probabilistic predictions and a required architecture for performing prognostics on critical aerospace systems. Prognosis is a critical element of a HM system and has the promise to realize major benefits for cost avoidance and safety improvement for fielded systems. It also presents a number of challenges to the HM system designer, primarily due to the need to properly model damage progression and to deal with large-grain uncertainty. Long-term prediction of a fault’s evolution to the point thatmay result in a failure requires means to represent and manage the inherent uncertainty. Moreover, accurate and precise prognosis demands good models of the fault growth and statistically sufficient samples of failure data to assist in training, validating, and fine tuning prognostic algorithms. Prognosis performance metrics, robust algorithms, and test platforms that may provide needed data have been the target of HM researchers in the recent past. Many accomplishments have been reported but major challenges still remain to be addressed. To address the issue of inherent uncertainties that are the aggregate of many unknowns and can result in considerable prediction variability, the concept of adaptive prognosis was introduced. In that case, available, albeit imperfect, information is used to update elements of the prognostic model. Only one of many approaches for accomplishing this was briefly introduced, namely, the particle filter. Other statistical update techniques include Bayesian updating, constrained optimization, and Kalman filtering. The design process is not a trivial process by which features and models are chosen for integration such that the best possible prediction on RUL still is obtained. It takes substantial effort to design systems so that measured data can be fused and used in conjunction with physics-based models to estimate current and future damage states. This is exacerbated when multiple models are employed that may use different feature inputs. The prognosis system must also be capable of intelligently calibrating a priori initial conditions (e.g., humidity, strain, and temperature) and random variable characteristics in an automated yet lucid process.