With the widespread application in industrial manufacturing and commercial services, well-trained deep neural networks (DNNs) are becoming increasingly valuable and crucial assets due to the tremendous training cost and excellent generalization performance. These trained models can be utilized by users without much expert knowledge benefiting from the emerging ''Machine Learning as a Service'' (MLaaS) paradigm. However, this paradigm also exposes the expensive models to various potential threats like model stealing and abuse. As an urgent requirement to defend against these threats, Deep Intellectual Property (DeepIP), to protect private training data, painstakingly-tuned hyperparameters, or costly learned model weights, has been the consensus of both industry and academia. To this end, numerous approaches have been proposed to achieve this goal in recent years, especially to prevent or discover model stealing and unauthorized redistribution. Given this period of rapid evolution, the goal of this paper is to provide a comprehensive survey of the recent achievements in this field. More than 190 research contributions are included in this survey, covering many aspects of Deep IP Protection: challenges/threats, invasive solutions (watermarking), non-invasive solutions (fingerprinting), evaluation metrics, and performance. We finish the survey by identifying promising directions for future research.