This research focuses on modeling curve-valued or functional data presenting regime changes. In this book we propose new probabilistic generative machine learning methodologies for curve modeling, classification, clustering and tracking. First, the models we propose for a single curve or independent sets of curves are based on specific regression models incorporating a flexible hidden process. They are able to capture non-stationary (dynamic) behavior within the curves and address the problem of missing information regarding the underlying regimes, and the problem of complex shaped classes. We then propose dynamic models for learning from curve sequences to make decision and prediction over time. The developed approaches rely on autoregressive dynamic models governed by hidden processes. The learning of the models is performed in both a batch mode (in which the curves are stored in advance) and an online mode as the learning proceeds (in which the curves are analyzed one at a time). The developed approaches have been used to addresses the problem of diagnosis and monitoring for predictive maintenance of the railway infrastructure.