This paper introduces a new generative deep learning network for human motion synthesis and control. Our key idea is to combine recurrent neural networks (RNNs) and adversarial training for human motion modeling. We first describe an efficient method for training an RNN model from prerecorded motion data. We implement RNNs with long short-term memory (LSTM) cells because they are capable of addressing the nonlinear dynamics and long term temporal dependencies present in human motions. Next, we train a refiner network using an adversarial loss, similar to generative adversarial networks (GANs), such that refined motion sequences are indistinguishable from real mocap data using a discriminative network. The resulting model is appealing for motion synthesis and control because it is compact, contact-aware, and can generate an infinite number of naturally looking motions with infinite lengths. Our experiments show that motions generated by our deep learning model are always highly realistic and comparable to high-quality motion capture data. We demonstrate the power and effectiveness of our models by exploring a variety of applications, ranging from random motion synthesis, online/offline motion control, and motion filtering. We show the superiority of our generative model by comparison against baseline models.