This paper discusses the Maximum Torque Per Ampere (MTPA) control of synchronous motors, which have become an indispensable part of highly-efficient motor drives. It explains the nature of torque produced by synchronous motors, ways to find its maximum and algorithms to operate at this point, despite changes of loads and motor parameter variations. The authors propose a classification of the MTPA methods, based on the features of each algorithm or group of similar methods. They demonstrate the conventional control scheme and discuss the modifications necessary for the implementation of each method. This paper reviews existing maximum torque per ampere control algorithms, discusses their pros and cons and suggests possible areas of usage for each group of methods. The authors of the paper share their vast experience in the industry and research aspects, which were obtained by developing industrial, commercial, traction and military drives, and report on their views on the perspective of each method taken into consideration.