Contemporary research has shown impetus in the diagnostics of permanent magnet (PM) type machines. The manufacturers are now more interested in building diagnostics features in the control algorithms of machines to make them more salable and reliable. A compact structure, exclusive high-power density, high torque density, and efficiency make the PM machine an attractive option to use in industrial applications. The impact of a harsh operational environment most often leads to faults in PM machines. The diagnosis and nipping of such faults at an early stage have appeared as the prime concern of manufacturers and end users. This paper reviews the recent advances in fault diagnosis techniques of the two most frequently occurring faults, namely inter-turn short fault (ITSF) and irreversible demagnetization fault (IDF). ITSF is associated with a short circuit in stator winding turns in the same phase of the machine, while IDF is associated with the weakening strength of the PM in the rotor. A detailed literature review of different categories of fault indexes and their strengths and weaknesses is presented. The research trends in the fault diagnosis and the shortcomings of available literature are discussed. Moreover, potential research directions and techniques applicable for possible solutions are also extensively suggested.