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Over the past few years, providers such as Google, Microsoft, and Amazon have started to provide customers with access to software interfaces allowing them to easily embed machine learning tasks into their applications. Overall, organizations can now use Machine Learning as a Service (MLaaS) engines to outsource complex tasks, e.g., training classifiers, performing predictions, clustering, etc. They can also let others query models trained on their data. Naturally, this approach can also be used (and is often advocated) in other contexts, including government collaborations, citizen science projects, and business-to-business partnerships. However, if malicious users were able to recover data used to train these models, the resulting information leakage would create serious issues. Likewise, if the inner parameters of the model are considered proprietary information, then access to the model should not allow an adversary to learn such parameters. In this document, we set to review privacy challenges in this space, providing a systematic review of the relevant research literature, also exploring possible countermeasures. More specifically, we provide ample background information on relevant concepts around machine learning and privacy. Then, we discuss possible adversarial models and settings, cover a wide range of attacks that relate to private and/or sensitive information leakage, and review recent results attempting to defend against such attacks. Finally, we conclude with a list of open problems that require more work, including the need for better evaluations, more targeted defenses, and the study of the relation to policy and data protection efforts.