The open-winding permanent magnet synchronous machines (OW-PMSMs) have recently been gaining more attention because of their fault-tolerant capability and power quality comparable to a 3-level converter-driven system. This paper reviews the common configurations of OW-PMSM when used as a generator, highlighting its shortcomings and benefits. The OW-PMSM with a common DC bus was found to be a promising direct-drive generator solution for wind energy conversion (WEC) systems considering fault tolerance, DC bus utilization, and power quality when appropriate control algorithms are in place. The presence of the zero-sequence current is the key disadvantage of the common DC bus configuration. The review highlights the algorithms that have been proposed to suppress the zero-sequence current of the OW-PMSM under healthy and various fault conditions, especially the open-circuit fault of semiconductor switch. Shutting down remotely located wind turbines because of faults, until they can be repaired, may not make economic sense. The OW-PMSM can offer the opportunity, to run a WEC system even under fault conditions albeit with low output power. This paper will assess the literature gaps in the existing control techniques that prevent the extension via a comprehensive review.