Urbanization changes the natural hydrological processes of a catchment through the replacement of the natural urban drainage network composed of creeks and ravines for an artificial one of streets, channels and stormwater drainage pipes. Since of middle 90's there has been a new concept to deal with stormwater named "SUDS" (sustainable urban drainage systems). In Chile there is evidence of this new paradigm since 1996. The paper reviews the main topics still unresearched in the field of urban drainage in Chile, relevant research and construction of SUDS projects as well as the advances in institutional, lawful and technical matter. The research was made through laws, technical and scientific published documents. Chile has carried out scientific projects and constructed public, private projects who consider sustainable urban drainage systems principles, the first area has been stormwater source control such as permeable pavements, green roofs, rain gardens and rain harvest, the second are public spaces and private neighborhoods. It is noted that the urban drainage topics to develop are stormwater quality, non-structural measures implementation, hydrological behavior of some structural measures in a home and city scale in a Chilean climatological context through hydrological and hydraulic modelling, temporal and spatial rainfall disaggregation, protection and the rehabilitation of urban streams.