The Landé g factor of highly charged Li-like and B-like ions has important applications in the development of HCI optical clocks, the diagnosis of nuclear fusion and astroplasma, the determination of physical constants, the test of the theory of multi-electron interaction, and the exploration of the QED effects, nuclear effects and various high-order effects in the extreme electromagnetic field environment. Based on Penning-trap technology, the experimental measurement accuracy of Landé g factor for Li-like and B-like ions has reached a very high level, and the experimental measurement accuracy is higher than the theoretical calculation accuracy. For the Li-like ions, the experimental measurements mainly focus on the 1s²2s ²S_1/2 state of Si¹¹⁺, Ca1⁷⁺and Sn4⁷⁺ions. Combined with the ab initio QED perturbation theory with the accuracy of 10-8 to 10-9, the contributions of one-loop QED, two-loop QED, screened QED effects, high-order electron correlation effects, and nuclear effects to the Landé g factor in the few-electron system are verified. The calculation accuracy is on the order of 10-6 combined with MCDHF and RCICP methods. For the 1s22p 2P_1/2 and 2P_3/2 states, the calculation accuracy is on the order of 10^-6 using ab initio QED perturbation theory. The calculation accuracy is also on the order of 10^-6 using a combination of the RCC and third-order MBPT methods. The B-like ions are five electron complex systems, and the electron-electron interaction and screened QED effects are particularly significant, so the theoretical calculation is more difficult than Li-like ions. The experimental measurements are mainly carried out around Ar1³⁺ and Sn⁴⁵⁺ ions. The accuracy calculated using expected value method is on the order of 10-5 to 10-6. The accuracy of the calculations is also on the order of 10^-5 to 10^-6 based on the third-order MBPT method. At present, the calculation results of ab initio QED perturbation theory for few-electron systems are in good agreement with the experimental values. But for the multi-electron complex system, the calculation is very complex and the amount of calculation is very large when the electron correlation effects, one-loop QED, two-loop QED, screened QED effects and nuclear effects are strictly solved. The expected value method can be applied to any atom and ion systems, and the calculation accuracy can reach the order of 10^-5 to 10^-6. However, this method only includes the low-order electron correlation effect, and does not consider the high-order QED effect, screened QED effects, and high-order nuclear correction. The calculation accuracy of Landé g factor for the few-electron system is lower than that of the ab initio QED perturbation theory. When existing calculation methods are extended to multi-electron complex systems, there are obvious differences in the application scope, calculation accuracy, and complete calculation of physical effects between various theoretical methods. It is difficult to take into account both the scope of application and the accuracy of calculation by using only one method. Therefore, based on the existing theoretical framework, the expected value method and ab initio QED perturbation theory can be combined to develop high-precision calculation methods of the Landé g factor for multi-electron complex systems, analyze the contribution of various high-order effects to the Landé g factor and improve the theoretical calculation accuracy, which is of great significance to promote the study of atomic properties and external field effects.