Industrial applications such as automation, robots, and electric vehicles are widely employing permanent magnet synchronous motors (PMSM) due to inherent characteristics such as high torque to power ratio, low maintenance, high efficiency, and wide operating range. However, PMSM drives can suffer from unwanted torque ripples caused by periodic disturbances of the electromagnetic effect. First, this article analyzes the sources of torque ripple in PMSMs. Second, the torque measurement techniques of the PMSM including torque sensors, torque observers, and indirect measurement methods are discussed to highlight their shortcomings. Third, this article categorizes and summarizes advanced control-based torque ripple minimization (CB-TRM) techniques for the PMSM by critically evaluating their impacts. These CB-TRM techniques actively control the current waveforms to ensure smooth torque generation and mitigate the effects of torque ripples. Finally, the article concludes by discussing remaining research questions and opportunities for future research on TRM techniques for PMSMs.