We review physical properties and potential applications of two-dimensional boron and carbon based nanostructures such as graphene and BC₃ sheet adsorbed with metal atoms, non-metal atoms or molecules. Pristine graphene is semi-metallic with zero band gap, which is nonmagnetic and has weak spin orbit coupling (SOC). BC₃ sheet is a semiconductor with an indirect band gap. As graphene and BC₃ sheet are adsorbed with metal atoms, non-metal atoms or molecules, graphene systems may have a band gap at Dirac point, strong SOC, magnetic order and superconductivity. Applications in hydrogen storage may be realized in graphene and BC₃ systems. In addition, it has been demonstrated that graphene can be used as gas sensors with significantly high precision.