Data hiding is the process of embedding information into a noise-tolerant signal such as a piece of audio, video, or image. Digital watermarking is a form of data hiding where identifying data is robustly embedded so that it can resist tampering and be used to identify the original owners of the media. Steganography, another form of data hiding, embeds data for the purpose of secure and secret communication. This survey summarises recent developments in deep learning techniques for data hiding for the purposes of watermarking and steganography, categorising them based on model architectures and noise injection methods. The objective functions, evaluation metrics, and datasets used for training these data hiding models are comprehensively summarised. Finally, we propose and discuss possible future directions for research into deep data hiding techniques.