In this thesis, we develop several novel degradation models based on techniques from functional data analysis. These models are suitable for characterizing different types of sensor-based degradation signals, whether they are censored at a certain fixed time point or truncated at the failure threshold. Our proposed models can also be easily extended to accommodate for the effects of environmental conditions on degradation processes. Unlike many existing degradation models that rely on the existence of a historical sample of complete degradation signals, our modeling framework is well-suited for modeling complete as well as incomplete (sparse and fragmented) degradation signals. We utilize these models to predict and continuously update, in real time, the residual life distributions of partially degraded components. We assess and compare the performance of our proposed models and existing benchmark models by using simulated signals and real world data sets. The results indicate that our models can provide a better characterization of the degradation signals and a more accurate prediction of a system's lifetime under different signal scenarios. Another major advantage of our models is their robustness to the model mis-specification, which is especially important for applications with incomplete degradation signals (sparse or fragmented).