As a representative reactor type of Generation IV nuclear energy systems, the sodium-cooled fast reactor (SFR) has become an international research hotspot due to its fuel breeding potential, transmutation capability of minor actinides, and inherent safety characteristics. However, its design and operation are universally subject to multi-source uncertainties, including nuclear data randomness, model simplification errors, and boundary condition perturbations. These uncertainties, when coupled with complex neutronics behavior within the reactor, sodium thermal-hydraulic characteristics, and multiphysics effects under accident conditions, may lead to deviations or abnormal fluctuations in the system response of SFR, and even trigger accident risks. This paper reviews research progress in SFR system uncertainty analysis from three aspects of reactor physics calculations, thermal-hydraulic analysis, and accident safety assessment. Worldwide research achievements, technical challenges and future development trends are summarized, and current research status and future directions of uncertainty analysis for SFR in China are analytically discussed. Through systematic analysis and synthesis, safety evaluation and design optimization of future SFR systems are perspectively provided.