The research presented in this dissertation is motivated by the need for balancing the increasing demand and limited capacity of the National Airspace System (NAS), and more generally for large scale networked dynamical systems. A new paradigm for building an Eulerian-Lagrangian Cell Transmission Model for air traffic flow is developed. It is based on a network flow model constructed from historical air traffic data, and is applied to the entire continental NAS in the United States. This model is called Large-capacity Cell Transmission Model, CTM(L), in reference to the Cell Transmission Model in highway traffic. The CTM(L) captures fundamental characteristics, for example aircraft counts in sectors and travel times, of traffic flows in the Air Traffic Control (ATC) system. The predictive capabilities of the model are successfully validated against the recorded Enhanced Traffic Management System (ETMS) and Aircraft Situation Display to Industry (ASDI) data by showing an accurate match between predicted sector counts (based on filed flight plans) and measured sector counts. Besides the CTM(L), four Eulerian network models are implemented to model high altitude air traffic flow. The four models are applied to high altitude traffic for six Air Route Traffic Control Centers (ARTCCs) in the NAS and surrounding airspace. Simulations are carried out for a full day of data for the models, to assess their predictive capabilities. The models' predictions are compared to the recorded flight data. Several error metrics are used to characterize the relative accuracy of the models. The efficiency of the respective models is also compared in terms of computational time and memory requirements for the scenarios of interest. Control strategies are designed and implemented on similar benchmark scenarios for two of the models. They use techniques such as adjoint-based optimization, and the mixed integer linear program (MILP). A discussion of the four models' structural differences explains why one model may outperform another. Finally, the CTM(L) model is used for NAS-wide optimal Traffic Flow Management (TFM). A problem of controlling sector aircraft count is posed as an integer program (IP) in which the dynamical system appears in the constraints. A problem specific algorithm based on a dual decomposition method is designed to show that the large scale optimization problem which has billions of variables and constraints, can be solved efficiently, making real-time NAS-wide TFM possible. The CTM(L) model and the optimization algorithm for NAS-wide TFM are integrated in FACET, a software developed at NASA Ames Research Center, in collaboration with Metron Aviation.