Flood disasters in urban underground spaces induced by extreme rainfall are becoming frequent. To reduce losses from flooding in underground spaces, it is essential to assess flood risks during extreme rainfall. This study focuses on flood disasters in urban underground spaces during extreme rainfall. First, the challenges encountered during the construction and operation phases of underground space development in terms of geology, technology, natural environment, and management are summarized. Second, a bibliometric analysis method is employed to review current risk research on flood risk assessment methods. The literature is clustered to clarify that current studies focus on three core aspects: danger, exposure, and vulnerability. Study hotspots for underground space flood disasters are analyzed from a temporal dimension. Furthermore, five risk assessment methods are summarized: (1) statistical analysis, (2) multicriteria decision making, (3) geographic information systems and remote sensing, (4) scenario-based analysis, and (5) machine learning analysis. The applicability, advantages, and limitations of each method are discussed. Based on the above, a conceptual framework for dynamic risk assessment of flood-propagation paths in underground spaces is proposed to predict flood paths and risk levels in real time. The proposed framework provides a theoretical basis for the effective management of flood disasters in underground spaces.