This paper addresses consensus problems for networks of dynamic agents with fixed and switching topologies and communication time-delays. It introduces two consensus protocols for networks with and without time-delays and provides convergence analysis for three cases: directed networks with fixed topology, directed networks with switching topology, and undirected networks with communication time-delays and fixed topology. The paper establishes a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance of a linear consensus protocol. It generalizes the notion of algebraic connectivity of undirected graphs to digraphs and shows that balanced digraphs play a key role in addressing average-consensus problems. A disagreement function is introduced as a Lyapunov function for the disagreement network dynamics. The paper provides analytical tools based on algebraic graph theory, matrix theory, and control theory. It demonstrates the effectiveness of the theoretical results through simulations. The paper also discusses the tradeoff between performance of reaching a consensus and robustness to time-delays. It shows that the maximum time-delay that can be tolerated by a network of integrators applying a linear consensus protocol is inversely proportional to the largest eigenvalue of the network topology or the maximum degree of the nodes of the network. The paper addresses consensus problems for networks with directed information flow and provides a convergence analysis for networks with switching topology. It also analyzes the effects of communication time-delays in undirected networks with fixed topology. The paper concludes with an outline of the paper's structure and main results.This paper addresses consensus problems for networks of dynamic agents with fixed and switching topologies and communication time-delays. It introduces two consensus protocols for networks with and without time-delays and provides convergence analysis for three cases: directed networks with fixed topology, directed networks with switching topology, and undirected networks with communication time-delays and fixed topology. The paper establishes a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance of a linear consensus protocol. It generalizes the notion of algebraic connectivity of undirected graphs to digraphs and shows that balanced digraphs play a key role in addressing average-consensus problems. A disagreement function is introduced as a Lyapunov function for the disagreement network dynamics. The paper provides analytical tools based on algebraic graph theory, matrix theory, and control theory. It demonstrates the effectiveness of the theoretical results through simulations. The paper also discusses the tradeoff between performance of reaching a consensus and robustness to time-delays. It shows that the maximum time-delay that can be tolerated by a network of integrators applying a linear consensus protocol is inversely proportional to the largest eigenvalue of the network topology or the maximum degree of the nodes of the network. The paper addresses consensus problems for networks with directed information flow and provides a convergence analysis for networks with switching topology. It also analyzes the effects of communication time-delays in undirected networks with fixed topology. The paper concludes with an outline of the paper's structure and main results.