The relative shift between graphene layers (d) significantly changes the electronic and optical properties of bilayer graphenes (BLGs). It induces band anticrossings, low-energy saddle points, the shift of subbands, and the change of state degeneracies of middle-energy saddle points. The number, frequencies, and spacings of peaks in single-particle excitation spectra are all affected by the relative shift. Moreover d induces anisotropy in the optical excitation, except for AA- and AB-stacked BLGs. The anisotropy and the d-dependent excitation spectra could be used to identify the interlayer shift.