We develop the scientific foundations and associated algorithmic tools for compactly representing and analyzing heterogeneous data streams from sensor/information-rich networked dynamical systems. We take a unified dynamics-based and data-driven approach for the design of passive and active monitors for anomaly detection in such systems. Dynamical models naturally capture temporal (i.e., causal) relations within data streams. Moreover, one can use hybrid and networked dynamical models to capture, respectively, logical relations and interactions between different data sources. We study structural properties of networks and dynamics to understand fundamental limitations of anomaly detection from data. By recasting information extraction problem as a networked hybrid system identification problem, we bring to bear tools from computer science, system and control theory and convex optimization to efficiently and rigorously analyze and organize information. The applications include diagnostics, anomaly and change detection in critical infrastructure such as building management systems, transportation and energy networks.