The use of power electronic converters is essential for the operation of Switched Reluctance Machines (SRMs). Many topologies and structures have been developed over the last years considering several specific applications for this kind of machine, improving the control strategies, performance range, fault-tolerant operation, among other aspects. Thus, due to the great importance of power electronic converters in such applications, this paper is focused on a detailed review of main structures and topologies for SRM drives. The proposed study is not limited to the classic two-level power converters topologies dedicated to the SRMs; it also presents a review about recent approaches, such as multilevel topologies and based on impedance source network. Moreover, this review is also focused on a new class of topologies associated to these machines, namely the ones with fault-tolerant capability. This new category of topologies has been a topic of research in recent years, being currently considered an area of great interest for future research work. An analysis, taking into consideration the main features of each structure and topology, was addressed in this review. A classification and comparison of the several structures and topologies for each kind of converter, considering modularity, boost capability, number of necessary switches and phases, integration in the machine design, control complexity, available voltage levels and fault-tolerant capability to different failure modes, is also presented. In this way, this review also includes a description of the presented solutions taking into consideration the reliability of the SRM drive.