Because of massively parallel distributed nature and very fast convergence rates, recurrent neural networks (RNN) are widely applied to solving many problems in optimization, control and robotic systems, etc. Hence, this book investigates the following RNN models which solve some practical problems, together with their corresponding analysis on stability and convergence. A type of multilayer pole-assignment neural networks is applied to online synthesizing and tuning feedback control systems. Then, a novel RNN model is established by absorbing the first-order time-derivative information to solve the Sylvester equation with time-varying coefficient matrices. A dual neural network is developed to handle quadratic programs subject to linear constraints. The Lagrangian neural network and primal-dual neural network are also reviewed for comparison purposes. The neural networks are then exploited for real-time motion planning of redundant manipulators. The publication is primarily intended for researchers and postgraduates studying in RNN, control and robotics.