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Communication networks have evolved from specialized research and tactical transmission systems to large-scale and highly complex interconnections of intelligent devices, increasingly becoming more commercial, consumer oriented, and heterogeneous. Propelled by emergent social networking services and high-definition streaming platforms, network traffic has grown explosively thanks to the advances in processing speed and storage capacity of state-of-the-art communication technologies. As "netizens" demand a seamless networking experience that entails not only higher speeds but also resilience and robustness to failures and malicious cyberattacks, ample opportunities for signal processing (SP) research arise. The vision is for ubiquitous smart network devices to enable data-driven statistical learning algorithms for distributed, robust, and online network operation and management, adaptable to the dynamically evolving network landscape with minimal need for human intervention. This article aims to delineate the analytical background and the relevance of SP tools to dynamic network monitoring, introducing the SP readership to the concept of dynamic network cartography? a framework to construct maps of the dynamic network state in an efficient and scalable manner tailored to large-scale heterogeneous networks.