The ever-growing advances of deep learning in many areas including vision, recommendation systems, natural language processing, etc., have led to the adoption of Deep Neural Networks (DNNs) in production systems. The availability of large datasets and high computational power are the main contributors to these advances. The datasets are usually crowdsourced and may contain sensitive information. This poses serious privacy concerns as this data can be misused or leaked through various vulnerabilities. Even if the cloud provider and the communication link is trusted, there are still threats of inference attacks where an attacker could speculate properties of the data used for training, or find the underlying model architecture and parameters. In this survey, we review the privacy concerns brought by deep learning, and the mitigating techniques introduced to tackle these issues. We also show that there is a gap in the literature regarding test-time inference privacy, and propose possible future research directions.