Inverter-fed induction motors (IMs) contain a serious of current harmonics, which become severer under stator and rotor faults. The resultant fault components in the currents affect the monitoring of the motor status. With this background, the fault components in the electromagnetic torque under stator faults considering harmonics are derived in this paper, and the fault components in current harmonics under rotor faults are analyzed. More importantly, the monitoring based on the fault characteristics (both in the torque and current) is proposed to provide reliable stator and rotor fault diagnosis. Specifically, the fault components induced by stator faults in the electromagnetic torque are discussed in this paper, and then, fault components are characterized in the torque spectrum to identify stator faults. To achieve so, a full-order flux observer is adopted to calculate the torque. On the other hand, under rotor faults, the sidebands caused by time and space harmonics in the current are analyzed and exploited to recognize rotor faults, being the motor current signature analysis (MCSA). Experimental tests are performed on an inverter-fed 2.2 kW/380 V/50 Hz IM, which verifies the analysis and the effectiveness of the proposed fault diagnosis methods of inverter-fed IMs.