In this paper we present the current status of modelling the time evolution of the transient conductivity of photoexcited semi-insulating (SI) 4H–SiC taking into account the properties of defect centres. A comprehensive model that includes the presence of six, the most significant, point defects occurring in SI 4H–SiC crystals is presented. The defect centres are attributed to the two kinds of nitrogen-related shallow donors, a boron-related shallow acceptor, deep electron and hole traps, and the Z_1/2 recombination centre. We present the results of the state-of-the-art numerical simulations showing how the photoconductivity transients change in time and how these changes are affected by the properties of defect centres. The properties of defect centres assumed for modelling are compared with the results of experimental studies of deep-level defects in high purity (HP) SI 4H–SiC wafers performed by the high-resolution photoinduced transient spectroscopy (HRPITS). The simulated photoconductivity transients are also compared with the experimental photocurrent transients for the HP SI 4H–SiC wafers with different deep-level defects. It is shown that a high-temperature annealing producing the C-rich material enables the fast photocurrent transients to be achieved. The presented analysis can be useful for technology of SI 4H–SiC high-power photoconductive switches with suitable characteristics.