We investigated band structures of alpha-graphyne and its derivative two-dimensional carbon compounds (2DCCs) via tight-binding approximations with "two-site" and "all-atom" models. The renormalized "two-site" model captures the band-gap features of alpha-graphyne and 2DCCs. This model suggests ways of tuning the band gaps of graphynes, namely, by adding adatoms or substituting the vertex sp(2) carbons with heteroatom. Because the "two-site" model cannot accurately reproduce first-principles results over a large range of wave vectors, we derived an "all-atom" model, which includes all p(z) orbitals in a unit cell. All atom tight-binding calculations show improved performances in describing the DFT band structures, and reveal that the flat bands in DFT band structures are mainly ascribed to the p(z) orbitals of the edge carbons. The results will help to uncover the underlying mechanisms of the band features of graphyne and 2DCCs and to design other graphyne-or graphdiyne-based 2DCCs for applications in the future. (C) 2013 AIP Publishing LLC.