Convolutional neural networks (CNNs) for computer vision, and recurrent neural networks (RNNs) for natural language processing.
Although this can be applied in other areas, RNNs have the advantage of networks that can have signals travelling in both directions by introducing loops in the network.
Feedback networks are powerful and can get extremely complicated. Computations derived from the previous input are fed back into the network, which gives them a kind of memory. Feedback networks are dynamic: their state is changing continuously until they reach an equilibrium point.