Optimizing the cost function in predictive control of multi-phase drives is computationally intensive. This poses a challenge since the required sampling period for drives falls within the microsecond range. Numerous methods have been proposed in the literature to address this computational demand. This paper reviews recent proposals for multi-phase drives of various kinds. A structured classification of the proposals is provided. Furthermore, an integrated framework is employed to cohesively present and connect previously unrelated methods. Key elements such as Allowed Control Set, inter-sample modulation, and weighting factor use are identified. New developments in multi-vector and single-vector approaches are discussed. Practical limitations for each approach are also considered.