Despite the emerging multi-phase and multi-level converters, two-level insulated gate bipolar transistor-based power converters are still widely used in industrial applications in nowadays. Thus, its reliability is of significant importance for ensuring industrial safety. In this paper, a review of the possibilities to ensure the reliable operation of these power converters is presented. The possible approaches are categorized into two groups: condition monitoring and fault-tolerant control. The former approach performs the monitoring methods of power converters, which enables the identification of device degradation to be realized. Accordingly, the mechanisms, indicators, and measuring methods of degradation are demonstrated in this paper to assist the design of condition-based maintenance. In contrast, the latter approach is a post-fault one, where power converters remain the operation by activating the fault-tolerant units after faults are identified. For this approach, fault detection, fault isolation, and tolerant strategies are essential. Finally, the performance and cost-effectiveness of the two categories are discussed in this paper.