Remaining Useful Life (RUL) prediction is a core approach to achieving Prognostics and Health Management (PHM) and a key technology for decision-making from preventive maintenance to predictive maintenance. As long life-cycle data become increasingly scarce and difficult to obtain in a short time, the prediction of RUL based on the tendency to performance degradation has emerged as an inevitable trend in the study of equipment reliability. As equipment is highly susceptible to external loads, operational stress, working conditions, and intrinsic wear, it undergoes continuous performance degradation with a nonlinear and time-varying degradation rate. Furthermore, equipment is subject to various uncertainties during operation, including those caused by external disturbances, measurement errors, and incomplete data collection, as well as inaccurate regression models used for RUL prediction. Considering the nonlinear, time-varying, and uncertainty during performance degradation process, dynamic and adaptive degradation tendency and RUL prediction models are developed based on the Relevance Vector Machine (RVM). The RVM method is essentially an approximation approach. Directly using RVM for prediction inevitably leads to low prediction accuracy. To address the limitations of evidence approximation in RVM, this chapter extends the RVM to a statistical manifold. First, degradation features are selected based on batch data. Then, a dynamic multi-step regression model is constructed, where the RVM model is extended to the statistical manifold to achieve more accurate degradation tendency prediction. Finally, the predicted degradation tendency is applied to estimate the RUL according to the First Hitting Time (FHT) method. Additionally, RVM model is limited to single-output variables, whereas real-world degradation processes are influenced by multiple variables. This chapter further extends the classical RVM model to a multivariate setting. Specifically, a multi-step RVM model is first established, where a matrix Gaussian distribution is introduced for the weight parameters in the RVM model. The unknown hyperparameters of the model are then estimated using the Nesterov accelerated gradient descent method. Then, the degradation tendency is predicted by the multivariate RVM approach. Finally, the RUL is estimated based on the predicted degradation tendency and the FHT method.