One of state-of-the-art recurrent neural networks (RNN) is dual neural network (DNN). It can solve quadratic programs (QP) in real time. The dual neural network is of simple piecewise-linear dynamics and has global (exponential) convergence to optimal solutions. In this chapter, we firstly introduce the QP problem formulation and its online solution based on recurrent neural networks. Some related concepts and definitions are also given. Secondly, we present the dual neural network and its design method. In addition to the general design method, for non-diagonal, non-analytical and/or time-varying cases, a matrix-inverse neural network could be combined into such a design procedure of dual neural network for online computation of its matrixinverse related term. Thirdly, we show the analysis results of dual neural networks. In addition to the general analysis results, we investigate the proof complexity of the exponential convergence condition of dual neural networks. Fourthly, we present the numerical simulation and illustrative example of using the dual neural network to solve static QP problems. Finally, we exploit the dual neural network to online solve motion planning problems of redundant robot manipulators, which is illustrated as engineering-application examples.