In real-time systems, data are often acquired sequentially, and repeatedly analyzed when more observations are added with time. A key challenge here is that memory and computational power cannot keep up with the increasing data size with time. Moreover, in many engineering applications, time-series data are often dynamic with time-evolving structures. Such structures should be properly modeled and exploited to facilitate learning and inference. Approaches that leverage dynamic structures of real-time systems are presented. The designed algorithms have recursions that are both memory and computationally efficient. We then see how our techniques facilitate inference over time-series data with dynamic structures from both theory and applications.