  Silicene, as the silicon analog of graphene, has been successfully fabricated
by epitaxial growing on various substrates. Similar to free-standing graphene,
free-standing silicene possesses a honeycomb structure and Dirac-cone-shaped
energy band, resulting in many fascinating properties such as high carrier
mobility, quantum spin Hall effect, quantum anomalous Hall effect, and quantum
valley Hall effect. The maintenance of the honeycomb crystal structure and the
Dirac cone of silicene is crucial for observation of its intrinsic properties.
In this review, we systematically discuss the substrate effects on the atomic
structure and electronic properties of silicene from a theoretical point of
view, especially focusing on the changes of the Dirac cone.
