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Condition monitoring in electric motor drives is essential for operation continuity. This article provides a review of fault detection and diagnosis (FDD) methods for electric motor drives. It first covers various types of faults, their mechanisms, and approaches to detect and diagnose them. The article categorizes faults into machine faults, power electronics (PE) faults, DC link capacitor faults, and sensor faults, and discusses FDD methods. FDD methods for machines are categorized as statistical methods, machine-learning methods, and deep-learning methods. PE FDD methods are divided into logic-based, residual-based, and controller-aided methods. DC link capacitor and sensor faults are briefly explained. Machine and PE faults are listed and presented as tables for easy comparison and fast referencing. Most papers are selected from the past five years but older references are added when necessary. Finally, a discussion section is added to reflect on current trends and possible future research areas.