As a result of climate change and urbanization, human activities are placing increasing pressure on nature, including with regard to urban stormwater runoff; consequently, various concepts related to urban stormwater runoff management have been proposed to tackle this problem in multiple countries. In this study, the latest research and techniques related to stormwater runoff management are reviewed in detail. A bibliometric analysis of proposed stormwater runoff management concepts developed from 2001 to 2021 was conducted based on a screening of 1771 studies obtained from the Web of Science (WoS). Bibliometric analysis is a research method that can be used to quantitatively analyze academic literature. Visualization of the data obtained from the literature using CiteSpace software and subsequent analysis of patent data through S-curve prediction were performed. The United States, China, and Australia were the top three countries from which publications on this issue were sourced. Each country tends to study its own most relevant issues and has a particularly clear understanding of its own research landscape. The development of stormwater runoff management concepts was analyzed using reference emergence analysis. This was followed by keyword clustering and keyword emergence analysis to identify current research hotspots, trends, technological developments, and limitations. The limitations and emerging trends related to current stormwater runoff management concepts are discussed thoroughly, and suggestions for future studies are provided.