The optimal control of electrical drives necessitates to take into account current and voltage limits that are imposed by the power electronics and the electrical machines. Let’s cite for example the flux-weakening operation of electrical drives for propulsion. If the control of classical three-phase drives Under voltage and current limits are known for a long time, the specific characteristics of multiphase drives open the way to researches on their control under such constraints. This paper aims to explain what are the main differences between three-phase and multiphase drives when they run under voltage and current constraints and try to show what are the scientific and technical problems to be solved. Some first results are given in order to show that Model Predictive Control (MPC) is expected to be a good candidate to answer the proposed challenge.