Abstract: Numerical stability has always been the bottleneck that plagues the wide application of lattice Boltzmann methods in the scenario of high Reynolds number and high Mach number flows. It has been a research hotspot and difficulty in the past three decades to improve the numerical stability and accuracy of the collision models for lattice Boltzmann methods. As an important branch of many collision models, the regularized collision model has made massive theoretical progress in recent years, and has been widely applied in the fields of high Reynolds number turbulent flow, high Mach number compressible flow and aeroacoustics flow. The present study systematically reviews the development history of regularized collision models, and establishes a systematic theoretical framework to illustrate the underlying theoretical connection among different regularized collision models. Meanwhile, the present work reveals the theoretical essence of the regularized multi-relaxation collision model, which is to rapidly relax the higher-order kinetic moments that cannot be expressed by the discrete lattice model in a coordinate-independent and self-similar moment space, so as to avoid the spurious modes affecting the hydrodynamic equations.