The Noise-Shaping (NS) SAR is an attractive new ADC architecture that emerged in the last decade. It combines the advantages of the SAR and the DSM architectures. NS SAR shows excellent potential for high efficiency and low cost, and is highly suited to process scaling. This paper gives an overview of the history of NS-SAR, reviews the fundamentals challenges, and summarizes the latest developments, including advanced loop filtering techniques, DAC mismatch mitigation, kT/C mitigation, and bandwidth boosting. A comprehensive comparison of the state-of-the-art NS-SAR ADCs is provided, and conclusions are derived.