Dynamically accurate torque control is an essential prerequisite for higher performance motor drive systems. For ac induction motors (IMs), the two most established strategies are direct torque control (DTC) and vector or field orientated control. DTC directly switches the inverter to regulate torque without requiring explicit stator current regulation. However, it suffers from variable switching frequency and is more challenging to implement in digital controllers. Vector control separately regulates the "torque" and "flux" producing components of the motor stator current and is readily suited to a digital implementation with a constant switching frequency. However, it requires accurate current control to be effective, typically achieved using a linear current regulation system. The principles of linear current regulation are well established and have been researched intensively over many years. However, their quantitative design is still an uncertain mix of theory and practice, including in particular how to best set the regulator gains. This paper addresses this issue, by presenting a precisely matched comparative analysis of three alternative PI, and a hysteresis-based, current regulation strategies, suitable for use in a "standard" vector control IM drive. The results show that properly tuned, all four strategies have essentially the same performance, suggesting that the choice between them needs really only be made on the basis of convenience of implementation and/or cost.