Over the last two decades, piezoelectric resonant sensors based on micro-electromechanical systems (MEMS) technologies have been extensively studied as such sensors offer several unique benefits, such as small form factor, high sensitivity, low noise performance and fabrication compatibility with mainstream integrated circuit technologies. One key challenge for piezoelectric MEMS resonant sensors is enhancing their quality factors (Qs) to improve the resolution of these resonant sensors. Apart from sensing applications, large values of Qs are also demanded when using piezoelectric MEMS resonators to build high-frequency oscillators and radio frequency (RF) filters due to the fact that high-Q MEMS resonators favor lowering close-to-carrier phase noise in oscillators and sharpening roll-off characteristics in RF filters. Pursuant to boosting Q, it is essential to elucidate the dominant dissipation mechanisms that set the Q of the resonator. Based upon these insights on dissipation, Q-enhancement strategies can then be designed to target and suppress the identified dominant losses. This paper provides a comprehensive review of the substantial progress that has been made during the last two decades for dissipation analysis methods and Q-enhancement strategies of piezoelectric MEMS laterally vibrating resonators.