An adversarial machine learning approach is introduced to launch jamming attacks on wireless communications and a defense strategy is presented. A cognitive transmitter uses a pre-trained classifier to predict the current channel status based on recent sensing results and decides whether to transmit or not, whereas a jammer collects channel status and ACKs to build a deep learning classifier that reliably predicts the next successful transmissions and effectively jams them. This jamming approach is shown to reduce the transmitter's performance much more severely compared with random or sensing-based jamming. The deep learning classification scores are used by the jammer for power control subject to an average power constraint. Next, a generative adversarial network (GAN) is developed for the jammer to reduce the time to collect the training dataset by augmenting it with synthetic samples. As a defense scheme, the transmitter deliberately takes a small number of wrong actions in spectrum access (in form of a causative attack against the jammer) and therefore prevents the jammer from building a reliable classifier. The transmitter systematically selects when to take wrong actions and adapts the level of defense to mislead the jammer into making prediction errors and consequently increase its throughput.