Abstract: Anticipation is the phenomenon in which a neural system generates responses ahead of the actual occurrence of the relevant stimulations. Obviously, anticipation is essential for the survival of living organism to compensate for the time delay induced by signal propagation/processing. A famous example is the anticipative arrival of a moving object (flash and lag effect) before its actual presence as perceived by our visual system. Recently, it is found that anticipation in our visual system can occur as early as in our retina. Although the retina is a relatively simple neural network, the basic mechanism of its anticipative capability is still far from clear. In this talk, we will review experiments on anticipative dynamics of retinas and discuss how our laboratory extends some of these works by using the concept of predictive information together with stochastic stimulations. Our main finding is that the retinal neural network can make use of the hidden information in stimulations generated by hidden Markov models to form anticipation while stimulations generated from Markov models (such as the Ornstein–Uhlenbeck process) cannot elicit anticipative responses from a retina. This last result might provide insights for the understanding of the anticipative mechanism of the retina in terms of its neural network.