In this talk, topics on complex dynamical network synchronization and its pinning control are presented.First, the concept of synchronization and some criteria are briefly introduced for various complex dynamical networks, including fully-connected, ring-shaped and star-shaped regular networks, as well as small-world and scale-free complex networks.Then, the issue of pinning-controlled synchronization is discussed, for complex networks that do not satisfy self-synchronized conditions.Furthermore, some commonly concerned questions are addressed, such as what kind of controllers to design, how many to use, and where to apply them on the network, so as to achieve effective network synchronization.Finally, a simple method is described for designing linear state-feedback pinning controller gains, verified and visualized by numerical simulation examples.