Single-atom catalysts (SACs) represent the ultimate size limit of nanoscale catalysts, combining the advantages of homogeneous and heterogeneous catalysts. SACs have isolated single-atom active sites that exhibit high atomic utilization efficiency, unique catalytic activity, and selectivity. Over the past few decades, synchrotron radiation techniques have played a crucial role in studying single-atom catalysis by identifying catalyst structures and enabling the understanding of reaction mechanisms. The profound comprehension of spectroscopic techniques and characteristics pertaining to SACs is important for exploring their catalytic activity origins and devising high-performance and stable SACs for industrial applications. In this review, we provide a comprehensive overview of the recent advances in X-ray based synchrotron radiation techniques for structural characterization and in situ/operando observation of SACs under reaction conditions. We emphasize the correlation between spectral fine features and structural characteristics of SACs, along with their analytical limitations. The development of IMST with spatial and temporal resolution is also discussed along with their significance in revealing the structural characteristics and reaction mechanisms of SACs. Additionally, this review explores the study of active center states using spectral fine characteristics combined with theoretical simulations, as well as spectroscopic analysis strategies utilizing machine learning methods to address challenges posed by atomic distribution inhomogeneity in SACs while envisaging potential applications integrating artificial intelligence seamlessly with experiments for real-time monitoring of single-atom catalytic processes.