The successive approximation register (SAR) is one of the most energy-efficient analog-to-digital converter (ADC) architecture for medium-resolution applications. However, its high energy efficiency quickly diminishes when the target resolution increases. This is because a SAR ADC suffers from several major error source, including the sampling kT/C noise, the comparator noise, and the DAC mismatch. These errors are increasing hard to address in high-resolution SAR ADCs. This paper reviews recent advances on error suppression techniques for SAR ADCs, including the sampling kT/C noise reduction, the noise-shaping (NS) SAR, and the mismatch error shaping (MES). These techniques aim to boost the resolution of SAR ADCs while maintaining their superior energy efficiency.