From the viewpoint of nonlinear dynamics, this review outlines the recent advances as well as some open problems in the study of neural networks with time delays, an important class of delayed systems in various neural network models. The survey includes three aspects as fellows: the dynamic features, available approaches and advances in research on most attractive problems. The evolution of a delayed neural network depends not only on the current state of the systems but also on previous ones. Hence, a delayed neural network should be modeled by a functional differential equation, the solution space of which is of infinite dimensions. Therefore, the dynamical behavior of delayed neural networks is very complex.