Since the first successful construction of negative index metamaterials in 2000,there is a growing interest in the study of metamaterials due to their potential applications in areas such as design of invisibility cloak and sub-wavelength imaging.In this talk,Ill first give a brief introduction to the short history of metamaterials.Then Ill focus on the mathematical modeling of metamaterials,and discuss some time-domain finite element schemes we developed in recent years.Finally,Ill conclude the talk with our cloak simulation and some open issues for further exploration.