Multilevel converters are commonly recommended for converting DC power to AC as per load requirements owing to several advantages such as common mode voltage, less distorted input current, low switching frequency and reduced THD. However, the reliability, performance and efficiency of MLIs depend in particular on the switching technique used. The Selective Harmonic Elimination PWM approach is more efficient among existing modulation techniques to remove undesired harmonics from the output of MLI, since it operates at low switching frequency, particularly at fundamental frequency. The fundamental switching frequency operation of SHEPWM reduce the switching losses and improves inverter efficiency. The principal problem, however, is the empirical approach to non-linear equations. Numerous algorithms have been developed and implemented over the last decades including computational approaches, analytical methods, algebraic methods and optimization algorithms to solve the SHE equations and to eliminate the unintended harmonics. This article presented various aspects of SHE problem formulations, the comprehensive philosophy of operation of various SHE problem-solving approaches and the application of multilevel inverters. PWM waveforms, with single and multiple transitions, are examined and shown at each voltage level for solution frameworks that suit multiple solutions for pulse width modulation to allow researchers gain a deeper understanding and solution of SHE problems.