While complexity and large-scale systems have always been important themes in systems and control theory, the current flowering of network dynamics and control was not so easy to predict. Two main reasons for the enormous research activity are the ubiquity of large-scale networks in a large number of application areas (from power networks to systems biology) and the happy marriage between on the one hand systems and control theory and algebraic graph theory on the other. In this talk we will concentrate on network dynamics with a clear physical structure. Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and associated Laplacian matrices. Several examples will be discussed, from mechanical systems to chemical reaction networks, and the common mathematical structure will be identified. Furthermore, it will be shown how this formulation leads to structure-preserving model reduction approaches. An attempt will be made to formulate open problems regarding scalability of analysis and control methodologies and connections to optimization.