Signal integrity and power integrity are the critical issues for high-speed digital circuits. This paper reviews the state-of-the-arts of the integral equation technique used for the simulation of signal integrity and power integrity including the power and ground planes. According to the different circuit boundary conditions, the applied integral equation methods can be classified into mode method/segment method, image method, and equivalent electromagnetic currents method. The mode/segment and image method is used for power and ground planes with rectangular shapes, while the equivalent electromagnetic currents method is efficient for power and ground planes with arbitrary shapes. The most important part of these integral equations is the integral kernels (Green's functions). The integral kernels are derived for different circuit boundaries. Both the theoretical formula and simulation results are present, which are then verified with other available simulation methods and measurement results.