An efficient electromagnetic modeling of multilayer microstrip antennas and circuits is presented. The surface integral equation is solved by using the method of moments. In this method, the multilayer Green's functions are efficiently evaluated by the discrete complex image method, and the higher-order basis functions defined on curvilinear triangular elements are employed to gain the fast convergence rate. To achieve the fast frequency sweep, the asymptotic waveform evaluation is incorporated into the analysis. To handle large-scale problems, two fast schemes are applied. One is the fast Fourier transform accelerated scheme, the adaptive integral method. The other is the multipole accelerated scheme, the multilevel fast multipole algorithm. Both of the algorithms reduce the memory requirement and the CPU time.