Autonomous navigation is achieved by training or programming the ship with the stored data about the vessel behavior in various sailing environment. The autonomous behaviour relies on intelligent analytics based on machine learning algorithms. As a major advance in machine learning, the deep learning approach is becoming a powerful technique for autonomy. The deep learning methodologies are applied in various fields in the maritime industry such as detecting anomalies, ship classification, collision avoidance, risk detection of cyber attacks, navigation in ports and so on. The present paper reviews on various methods available in the literature for vessel autonomy and their applications in ship navigation. The focus of the work is to illustrate the advantages of deep learning approach over the machine learning and other traditional methods.