A general overview of Noise-Shaping Successive Approximation Register (SAR) analog-to-digital converters is provided, encompassing the fundamentals, operational principles, and key architectures of Noise-Shaping SAR (NS SAR). Key challenges, including inherent errors in processing circuits, are examined, along with current advancements in architecture design. Various issues, such as loop filter optimization, implementation methods, and DAC network element mismatches, are explored, along with considerations for voltage converter performance. The design of dynamic comparators is examined, highlighting their critical role in the SAR ADC architecture. Various architectures of dynamic comparators are extensively explored, including optimization techniques, performance considerations, and emerging trends. Finally, emerging trends and future challenges in the field are discussed.