In this dissertation, we study the problems of structure design and optimal control of consensus and synchronization networks. Our objective is to design controller that utilize limited information exchange between subsystems in large-scale networks. To obtain controllers with low communication requirements, we seek solutions to regularized versions of the H2 optimal control problem. The proposed framework can be leveraged for control design in applications like wide-area control in bulk power systems, frequency regulation in power system/microgrids, synchronization of nonlinear oscillator networks, etc. The structure of the dissertation is organized as follows. In Part I, we focus on the optimal control problems in systems with symmetries and consensus/synchronization networks. They are characterized by structural constraints that arise either from the underlying group structure or the lack of the absolute measurements for a part of the state vector. Our framework solves the regularized versions of the H2 optimal control problems that allow the state-space representations that are used to quantify the system’s performance and sparsity of the controller to be expressed in different sets of coordinates. For systems with symmetric dynamic matrices, the problem of minimizing the H2 or Hinfinity performance of the closed-loop system can be cast as a convex optimization problem. Studying the symmetric component of a general system’s dynamic matrices provides bounds on the H2 and Hinfinity performance of the original system. Part II studies wide-area control of inter-area oscillations in power systems. Our input-output analysis examines power spectral density and variance amplification of stochastically forced systems and offers new insights relative to modal approaches. To improve upon the limitations of conventional wide-area control strategies, we also study the problem of signal selection and optimal design of sparse and block-sparse wide- area controllers. We show how different sparsity-promoting penalty functions can be used to achieve a desired balance between closed-loop performance and communication complexity. In particular, we demonstrate that the addition of certain long-range communication links and careful retuning of the local controllers represent an effective means for improving system performance. In Part III, we apply the sparsity-promoting optimal control framework to two problem encounters in distributed networks. First, we consider the optimal frequency regulation problem in power systems and propose a principled heuristic to identify the structure and gains of the distributed integral control layer. We define the proposed distributed PI-controller and formulate the resulting static output-feedback control problem. Second, we develop a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The structured optimal-control problem allows us to seek a decentralized control strategy that precludes communications between the weakly nonlinear Lienard-type oscillators.