With great success of graphene, a novel two-dimensional honeycomb lattice has been explored. Silicene, a honeycomb lattice of silicon atoms, is a candidate as an innovative material as it can acquire not only the Dirac fermion characters but exotic properties of the topological insulator. Recently, silicene has been synthesized on the Ag(111) surfaces. We review the state-of-the-art, including our recent achievements, of silicene grown on Ag (111). By using scanning tunneling microscopy/spectroscopy (STM /STS), low-energy electron diffraction (LEED), and density functional theory (DFT) calculations, we have revealed the geometric and electronic structures of the single layer silicene. We have found that the interaction between the silicene and the underlying Ag substrate is strong, and thus silicene on Ag surfaces loses the Dirac fermion character.