Changes in extreme precipitation should be one of the primary impacts of climate change (CC) in urban areas. To assess these impacts, rainfall data from climate models are commonly used. The main goal of this paper is to report on the state of knowledge and recent works on the study of CC impacts with a focus on urban areas, in order to produce an integrated review of various approaches to which future studies can then be compared or constructed. Model output statistics (MOS) methods are increasingly used in the literature to study the impacts of CC in urban settings. A review of previous works highlights the non-stationarity nature of future climate data, underscoring the need to revise urban drainage system design criteria. A comparison of these studies is made difficult, however, by the numerous sources of uncertainty arising from a plethora of assumptions, scenarios, and modeling options. All the methods used do, however, predict increased extreme precipitation in the future, suggesting potential risks of combined sewer overflow frequencies, flooding, and back-up in existing sewer systems in urban areas. Future studies must quantify more accurately the different sources of uncertainty by improving downscaling and correction methods. New research is necessary to improve the data validation process, an aspect that is seldom reported in the literature. Finally, the potential application of non-stationarity conditions into generalized extreme value (GEV) distribution should be assessed more closely, which will require close collaboration between engineers, hydrologists, statisticians, and climatologists, thus contributing to the ongoing reflection on this issue of social concern.