State‐of‐the‐art model‐based predictive control techniques for AC motor drives are reviewed in this paper. A plethora of MPC algorithms with vast number of complex ideas has emerged in the last decade and this work makes an attempt to present those concepts in an intuitive, comprehensive and hierarchical manner. More emphasis is laid on finite control set model predictive control (FCS‐MPC) methods, especially predictive torque control (PTC) and predictive current control (PCC) because of their emergence as the prime focus of ongoing research in energy efficient drive control. The main focus of this review is to analyse the most recent work, signpost the future research directions, identify the core challenges and consolidate the ideas into a coherent and concise reference. A comprehensive classification based on actuation signals is presented and reviewed in detail. Then, the important challenges in MPC implementation, such as computational complexity reduction and delay compensation, weighting factor selection for multi‐objective cost functions, steady state performance and ripple reduction, parameter variations/model mismatching and achieving extended prediction horizons, are surveyed and most relevant solutions are reviewed. A detailed analysis of the last five years related work is given at the end and it is concluded that the future course seems to be diverting towards voltage vector selection with optimised phase, magnitude and duty ratios. Computational burden is still one of the main hurdle towards MPC proliferation and adaptation in AC drive control at the industrial level. However, with advent of high speed and cheaper signal processors and development of efficient algorithms, MPC is rapidly becoming the control method of choice for energy‐efficient drive control.