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Distributed machine learning (DML) techniques, such as federated learning, partitioned learning, and distributed reinforcement learning, have been increasingly applied to wireless communications. This is due to improved capabilities of terminal devices, explosively growing data volume, congestion in the radio interfaces, and increasing concern of data privacy. The unique features of wireless systems, such as large scale, geographically dispersed deployment, user mobility, and massive amount of data, give rise to new challenges in the design of DML techniques. There is a clear gap in the existing literature in that the DML techniques are yet to be systematically reviewed for their applicability to wireless systems. This survey bridges the gap by providing a contemporary and comprehensive survey of DML techniques with a focus on wireless networks. Specifically, we review the latest applications of DML in power control, spectrum management, user association, and edge cloud computing. The optimality, scalability, convergence rate, computation cost, and communication overhead of DML are analyzed. We also discuss the potential adversarial attacks faced by DML applications, and describe state-of-the-art countermeasures to preserve privacy and security. Last but not least, we point out a number of key issues yet to be addressed, and collate potentially interesting and challenging topics for future research.