This chapter considers synchronization of networked nonlinear dynamical systems under switching communication topologies. In particular, the agent dynamics are unstable and the interaction graph is time-varying with weak connectivity. We first give definitions on consensus and synchronization and present the considered problem. Then, the case of a directed graph with the uniform joint connectivity is considered. We establish a sufficient condition for reaching global exponential synchronization in terms of the relationship between the global Lipschitz constant and the network parameters. Moreover, for the case of an undirected graph with infinite joint connectivity, we show that the commonly used Lipschitz condition on the nonlinear self-dynamics is not sufficient to ensure synchronization even for an arbitrarily large coupling strength. By relaxing the global Lipschitz condition to the global Lipschitz-like condition, a sufficient synchronization condition is established in terms of the times of connectivity, the integral of the Lipschitz gain, and the network parameters.