Abstract：In the June 23, 2006’s issue of Science magazine, Pendry et al. and Leonhardt independently published their work on electromagnetic cloaking. In Nov.10, 2006’s Science, Pendry et al. demonstrated the first practical realization of such a cloak with the use of artificially structured metamaterials. Since then, there is a growing interest in using metamaterials to construct invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, and then focus on some cloaking models. Well-posedness study and time domain numerical simulations will be presented.