We present our vision for a departure from the established way of architecting and assessing communication networks, by incorporating the semantics of information, defined not necessarily as the meaning of the messages, but as their significance, possibly within a real-time constraint, relative to the purpose of the data exchange. We argue that research efforts must focus on laying the theoretical foundations of a redesign of the entire process of information generation, transmission, and usage for networked systems in unison by developing advanced semantic metrics for communications and control systems; an optimal sampling theory combining signal sparsity and timeliness, for real-time prediction/reconstruction/control under communication constraints and delays; temporally effective compressed sensing techniques for decision making and inference directly in the compressed domain; and semantic-aware data generation, channel coding, packetization, feedback, and multiple and random access schemes that reduce the volume of data and the energy consumption, increasing the number of supportable devices. This paradigm shift targets jointly optimal information gathering, information dissemination, and decision making policies in networked systems.