Induction motors make up approximately 80% of the electric motors in the railway sector due to their robustness, high efficiency, and low maintenance cost. Nevertheless, these motors are subject to failures which can lead to costly downtime and service interruptions. In recent years, there has been a growing interest in developing fault diagnosis systems for railway traction motors using advanced non-invasive detection and data analysis techniques. Implementing these methods in railway applications can prove challenging due to variable speed and low-load operating conditions, as well as the use of inverter-fed motor drives. This comprehensive review paper summarizes general methods of fault diagnosis for induction machines. It details the faults seen in induction motors, the most relevant signals measured for fault detection, the signal processing techniques for fault extraction as well as some classification algorithms for diagnosis purposes. By giving the advantages and drawbacks of each technique, it helps select the appropriate method that could address the challenges of railway applications.