In the context of global climate change and urban expansion, urban floods frequently cause serious social problems and economic losses. Flood risk assessment as the main content of urban flood management has received extensive attention. This article first presents the conceptual framework of urban flood risk assessment and the function of hazard, exposure, and vulnerability. It then reviews their main research contents respectively, analyzes the strengths and limitations of different research methods in the perspective of urban flood risk management. We conclude that the development trends of urban flood risk assessment include the following four aspects: 1) With regard to flood hazard evaluation, developing the two-dimensional hydraulics flood inundation model incorporating different sources of floods in urban areas such as pluvial, fluvial, and coastal floods is imperative for urban flood risk assessment. 2) Exposure evaluation is moving towards more refined and dynamic evaluation with the support of big data and GIS. 3) Vulnerability assessment is shifting from the quantitative evaluation of the physical dimension to multi- dimensional assessments, such as social, economic, cultural, environmental, and others. 4) In addition, semi- quantitative and quantitative urban flood risk assessment combined with climate change and urban expansion considerations under multiple scenarios is also an important component of future urban flood management.