Induction motors are widely used worldwide for domestic and industrial applications. Fault detection and classification techniques based on signal analysis have increased in popularity due to the growing use of induction motors in new technologies such as electric vehicles, automatic control, maintenance systems, and the inclusion of renewable energy sources in electrical systems, among others. Hence, monitoring, fault detection, and classification are topics of interest for researchers, given that the presence of a fault can lead to catastrophic consequences concerning technical and financial aspects. To detect a fault in an induction motor, several techniques based on different physical variables, such as vibrations, current signals, stray flux, and thermographic images, have been studied. This paper reviews recent investigations into physical variables, instruments, and techniques used in the analysis of faults in induction motors, aiming to provide an overview on the pros and cons of using a certain type of physical variable for fault detection. A discussion about the detection accuracy and complexity of the signals analysis is presented, comparing the results reported in recent years. This work finds that current and vibration are the most popular signals employed to detect faults in induction motors. However, stray flux signal analysis is presented as a promising alternative to detect faults under certain operating conditions where other methods, such as current analysis, may fail.