Due to their efficiency and control capabilities, induction motors fed with inverters have become prevalent in various industrial applications. However, ensuring the reliable operation of the motor and diagnosing faults on time are crucial for preventing unexpected failures and minimizing downtime. This paper systematically analyzes condition monitoring and practical diagnostic techniques for inverter-fed motor drive systems. This study encompasses a thorough evaluation of different methods used for condition monitoring and diagnostics of induction motors, with the most crucial faults in their stator, rotor, bearings, eccentricity, shaft currents, and partial discharges. It also includes an assessment of their applicability. The presented analysis includes a focus on the challenges associated with inverter-fed systems, such as high-frequency harmonics, common-mode voltages causing the bearing currents, and high voltage gradients (dv/dt) due to fast switching frequency, which can impact the motor operation, as well as its faults analysis. Furthermore, this research explores the usefulness and efficiency of various available diagnostic methods, such as motor current signature analysis and other useful analyses using advanced signal processing techniques. This study aims to present findings that provide valuable insights for developing comprehensive condition monitoring strategies, and practical diagnostic techniques that enable proactive maintenance, enhanced system performance, and improved operational reliability of inverter-fed motor drive systems.