High power medium voltage drives covers power ratings from 1 MW to 100MW and at the medium voltage level of 2.3KV to 13.8 KV. They have been receiving greater attention in the past few decades for high power applications due to their high efficiency, high reliability, effective fault protection, high dynamic performance, regenerative braking capacity and four quadrant operation. This paper provides an over view on commonly used CSI topology in MV drives. In High power MV drives maximum switching frequency is limited due to thermal losses this leads to production of lower order of the unwanted harmonics in PWM CSI output current. The most effective modulation technique to eliminate lower order of harmonics is Selective Harmonic Elimination (SHE). Finally in this paper recent research progress in the area of SHE modulation technique is reviewed.