Abstract: This chapter aims at providing an insight into simulations of microwave heating scenarios with both the FDTD and FEM algorithms in order to make advanced modelling easier and better understood. Several examples are provided to better illustrate the basic concepts of the modelling methods. Properties important in the analysis of microwave power phenomena are stressed and shown to affect the computational accuracy when handled improperly. The specific topics presented in subsequent sections include background of the modelling methods, with emphasis on mechanisms useful in coupled multi-physics analysis, error bounds due to numerical dispersion inherent to numerical algorithms, modelling of lossy materials crucial in the analysis of the microwave heating effect, modelling of dispersive media, and coupled analysis of microwave heating involving thermal variations of material parameters, heat conduction and load rotation effects besides the EM phenomena.