Inertial sensing is used in many applications and platforms, ranging from day-to-day devices such as smartphones to very complex ones such as autonomous vehicles. In recent years, the development of machine learning and deep learning techniques has increased significantly in the field of inertial sensing and sensor fusion. This is due to the development of efficient computing hardware and the accessibility of publicly available sensor data. These data-driven approaches mainly aim to empower model-based inertial sensing algorithms. To encourage further research in integrating deep learning with inertial navigation and fusion and to leverage their capabilities, this paper provides an in-depth review of deep learning methods for inertial sensing and sensor fusion. We discuss learning methods for calibration and denoising as well as approaches for improving pure inertial navigation and sensor fusion. The latter is done by learning some of the fusion filter parameters. The reviewed approaches are classified by the environment in which the vehicles operate: land, air, and sea. In addition, we analyze trends and future directions in deep learning-based navigation and provide statistical data on commonly used approaches.