Abstract: Scientific description requires mathematical modeling, while conventional mathematical modelingand quantitative analysis depend on characteristic scales. Complex systems such as cities usually bear no characteristic scale, and thus cannot be effectively described with mathematical methods. In this case, characteristic scale analyses should be replaced by scaling analysis. The studies on urban scaling originates from the uncertainty of spatial measurements in the geographical world. The mathematical essence of scaling in cities lies in the invariance in scaling transformation, that is, dilation symmetry. In recent years, scaling has become a hot topic and frontier in theoretical research and empirical analyses on cities. The main research fields include allometric scaling, hierarchical scaling, spatial scaling and network scaling. Fractal geometry is one of powerful tools for scaling analysis. Urban scaling research has made remarkable achievement, but also leads to a series of problems, including over identification of scaling, limited construction of theoretical models, dependence of scaling exponents on the definition of the study area, and lack of organic connection between various branch domains. Scaling represents the new direction of urban theoretical research and method development. In the future, it will complement and cooperate with the urban theoretical modeling based on characteristic scales.