Abstract: The correlation between space charge kinetics, which involve both physical mechanism and experimental observation, as well as electrical insulation characteristics in polymers under a strong electric field is a research focus in the field of high voltage insulation. The signal quality, spatial resolution, and measurement speed of the existing space charge measurement technologies cannot meet the actual engineering requirements; while the numerical simulation of space charge kinetics can provide abundant data and discover universal properties, which are unavailable from measurement, making it promising to determine the dominant classical electrical conduction model, assist unveiling the insulation aging mechanism, direct the product design, and predict the service time. This review firstly introduced the basic theory of space charge kinetics in polymeric insulation and the general form of mathematical equations, summarized the simulation models of space charge for two typical insulation structures, and discussed the features of common numerical algorithms. Then, preliminary applications of the numerical simulation of space charge were presented, including fundamental electrical properties, space charge packet phenomenon, and electrical tree aging. Finally, future researches on the numerical simulation of space charge kinetics were prospected, including refining the models and algorithms, extracting microscopic material parameters, proposing the route of multi-scale simulation, and measuring the space charge in large-size and multi-layer insulation.