1) Six-step drive, This is a simple method. They are preferred at high speeds and high powers. it has high harmonic spectrum which can be reduced by using many methods.
2) Sinusoidal switching method.
3) The vector control. The most commonly used method. it has low harmonic spectrum. Its application is difficult and involves high mathematical expressions.
The AC machine drive systems are separated into two different sections which are aptly called scalar and vector control. A simple control method is the constant V/f method where V is the stator voltage and f is the operating frequency. The method is mostly applied to Induction Motor drive system. In addition, there is a wide range of control approaches for inverter switching in the field oriented control (FOC) area. All proposed methods in the FOC are based on a constant linkage flux during machine operation.
Furthermore, the vector control is divided into two different branches named Direct Torque Control (DTC) and Field Oriented Control (FOC). Also, the FOC consists of two different families called Direct and indirect FOC. There is a wide range of control approaches for inverter switching in the FOC area. All proposed methods in the FOC are based on a constant linkage flux during machine operation. In addition, The direct self-control and space vector modulation are two different control approaches which are categorized in the DTC control scheme. You can find large numbers of literature by surfing outstanding journals on the internet. Besides, I want to suggest it will help you if you read a book entitled "vector control of AC machines" by P. Vas.
in addition to all those answers, all the methods are applicable in industry, it depends on application, for example vector control is not suitable for multi-motors drive, instead, open loop V/F control is used. DTC is perfect for fast torque developing application but it requires very fast and powerful processors, moreover the switching losses are high due to the uncontroller switching frequency. you should select the control method according to your application and not vice versa.