In this paper, we, respectively, solve the problems of event-triggered pinning synchronization and robust pinning synchronization of multiple weighted coupled neural networks (MWCNNs). By devising suitable event-triggered controller, some pinning synchronization and robust pinning synchronization criteria for MWCNNs with the appropriate event-triggered condition are deduced, respectively, on the basis of some inequalities and the theory of Lynapunov functional. Furthermore, we research the event-triggered pinning synchronization and event-triggered robust pinning synchronization of multiple weighted coupled delayed neural networks and establish some correlative synchronization criteria, respectively, on the basis of appropriate event-triggered condition and pinning controller. At last, the numerical simulation results in two examples verify the validity of the theoretical results.