Abstract: Because of the strong coupling between the spin, orbital, and lattice degrees of freedom, multiferroic materials display very rich and novel physics. However, first-principles methods so far still cannot be applied directly to study the finite temperature properties of multiferroic materials. The first-principles effective Hamiltonian methods, on the contrary, can be used. In this review we introduce these methods and their applications in studying the phase diagrams of magneto-ferroelectrics RMn₂O₅ and CuO, and the electromagnon in RMn₂O₅.