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Ferroelectric and multiferroic materials form an important class offunctional materials. Over the last twenty years, first-principles-basedeffective Hamiltonian approaches have been successfully developed to simulatethese materials. In recent years, effective Hamiltonian approaches were furthercombined with molecular dynamics methods to investigate terahertz dynamicalproperties of various perovskites. With this combination, a variety offerroelectric and multiferroic materials, including BaTiO_{3}, Ba(Sr,Ti)O_{3},Pb(Zr,Ti)O_{3}, BiFeO_{3}, and SrTiO_{3} bulks and films have been simulated,which led to the understanding of complex phenomena and discovery of noveleffects. In this review, we first provide technical details about effectiveHamiltonians and molecular dynamics simulation. Then, we present applicationsof the combination of these two techniques to different perovskites. Finally,we also briefly discuss possible future directions of this approach.

Terahertz dielectric response and coupled dynamics of ferroelectrics and multiferroics from effective Hamiltonian simulations