The magnetohydrodynamic (late-time) electromagnetic pulse (E3) generated by high-altitude nuclear explosions has a serious impact on national key infrastructures such as the power system. Due to the complex mechanism of late-time electromagnetic pulse generation and many dependent factors, including explosion yield, explosion height, explosion orientation, explosion time, observation point position and soil conductivity, there is no available mature code that can simulate the whole generation process of late-time electromagnetic pulse. This paper introduces the generation mechanism of late-time electromagnetic pulse, discusses the relationship between the electric field of late-time electromagnetic pulse and the change of explosive yield of nuclear devices, explosive height, and atmospheric conditions. The electric field peak of E3A increases linearly with the explosion equivalent, while the electric field peak of E3B shows obvious saturation effect with the explosion equivalent increase. The current status of the simulation code of late-time electromagnetic pulse is analyzed, and it can provide a reference for further research on the numerical simulation method and code development of late-time electromagnetic pulse.