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The newly emerged machine learning (e.g., deep learning) methods have become a strong driving force to revolutionize a wide range of industries, such as smart healthcare, financial technology, and surveillance systems. Meanwhile, privacy has emerged as a big concern in this machine learning-based artificial intelligence era. It is important to note that the problem of privacy preservation in the context of machine learning is quite different from that in traditional data privacy protection, as machine learning can act as both friend and foe. Currently, the work on the preservation of privacy and machine learning are still in an infancy stage, as most existing solutions only focus on privacy problems during the machine learning process. Therefore, a comprehensive study on the privacy preservation problems and machine learning is required. This article surveys the state of the art in privacy issues and solutions for machine learning. The survey covers three categories of interactions between privacy and machine learning: (i) private machine learning, (ii) machine learning-aided privacy protection, and (iii) machine learning-based privacy attack and corresponding protection schemes. The current research progress in each category is reviewed and the key challenges are identified. Finally, based on our in-depth analysis of the area of privacy and machine learning, we point out future research directions in this field.