The RNNs (Recurrent Neural Networks) are a general case of arti cial neural networks where the connections are not feed-forward ones only. In RNNs, connections between units form directed cycles, providing an implicit internal memory. Those RNNs are adapted to problems dealing with signals evolving through time. Their internal memory gives them the ability to naturally take time into account. Valuable approximation results have been obtained for dynamical systems.During the last few years, several interesting neural networks developments have emerged such as spike nets and deep networks. This book will show that a lot of improvement and results are also present in the active eld of RNNs.