The problems of modeling of the rotational motion of the Earth are considered in the framework of general relativity. Both, rigid and deformable bodies are discussed. Rigorous definitions of the tensor of inertia, Tisserand-like axes and the angular velocity of rotation of an extended deformable body moving and rotating in external gravitational fields are proposed in the first post-Newtonian approximation. The implications of these post-Newtonian definitions on modeling of Earth rotation are analyzed.