The resonant X-ray scattering (RXS) and the resonant inelastic X-ray scattering (RIXS) in correlated electron systems with the orbital degree of freedom are reviewed from the theoretical view points. In the first part, the orbital order and RXS as an experimental tool to detect the orbital order are reviewed. We introduce characteristic interacting-orbital models and orbital orders, in which a unique orbital frustration effect emerges. As a case study, the theoretical and experimental studies in an impurity effect on the orbital order are presented. In the second part, the RIXS studies for observation of the orbital excitation are reviewed. In particular, we focus on the polarization dependence of RIXS which is crucial to identify the scattering from the orbital excitation. We introduce the recent progresses of the collective orbital excitations coupled with the lattice vibration. The non-resonant inelastic X-ray scattering as a tool to detect the orbital excitations is also reviewed.