Numerical Simulations of Phase Transitions　-- from equilibrium to non-equilibrium

We briefly review our recent activities in Monte Carlo simulations andmolecular dynamics simulations of phase transitions.We start from second order transitions, then come to Kosterlitz-Thoulesstransitions, first order transitions and melting transitions etc.Effects of the quenched disorder and frustrations will be studied.Simulations in both equilibrium and non-equilibrium states arepresented, but non-equilibrium dynamic behavior will be emphasized.