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Machine learning (ML) provides effective means to learn from spectrum data and solve complex tasks involved in wireless communications. Supported by recent advances in computational resources and algorithmic designs, deep learning (DL) has found success in performing various wireless communication tasks such as signal recognition, spectrum sensing and waveform design. However, ML in general and DL in particular have been found vulnerable to manipulations thus giving rise to a field of study called adversarial machine learning (AML). Although AML has been extensively studied in other data domains such as computer vision and natural language processing, research for AML in the wireless communications domain is still in its early stage. This paper presents a comprehensive review of the latest research efforts focused on AML in wireless communications while accounting for the unique characteristics of wireless systems. First, the background of AML attacks on deep neural networks is discussed and a taxonomy of AML attack types is provided. Various methods of generating adversarial examples and attack mechanisms are also described. In addition, an holistic survey of existing research on AML attacks for various wireless communication problems as well as the corresponding defense mechanisms in the wireless domain are presented. Finally, as new attacks and defense techniques are developed, recent research trends and the overarching future outlook for AML for next-generation wireless communications are discussed.