Phase oscillators with pulsatile interactions are powerful and popular models describing networks of various nature among which neuronal populations are a prototypical example. The advantages of such models are their simple numerical implementation, low dimension and possibility for theoretical analysis. Recently, pulse-coupled phase oscillators have been shown to be especially useful for study of the networks with coupling delays. It has been proven that networks of phase oscillators with time-delay pulsatile coupling can be reduced to finite dimensional maps under quite general conditions. With the help of this technique we investigate dynamics of networks of various configurations. The studied phenomena include one-to-one and cross-frequency synchronization of two oscillators, pattern formation in small networks, global synchronization in large networks with all-to-all coupling and multi-level activity of networks with clustered structure.