In this chapter, the formulations of precession-nutation and polar motion of the rigid and elastic Earth models are formulated in detail. For the rigid Earth model, the precession-nutation and polar motion caused by the lunisolar gravitational attraction are first presented, and then the normal modes of rotation including the Eulerian wobble, the axial spin mode, and the tilt-over mode are presented. For the elastic Earth model, the deformation caused by the variation of the Earth rotation, notably the pole tide, is formulated, and then the precession-nutation and polar motion caused by the lunisolar gravitational attraction, as well as the normal modes of rotation, are formulated. Lastly, the variation of the Earth rotation as a result of the interaction between the solid Earth and the atmosphere-hydrosphere-cryosphere system is formulated for the elastic Earth model, and then the up-to-date theory is introduced by incorporating the effects of mantle anelasticity (i.e., non-pure elasticity) and the Earth’s core. As an application, the Earth rotation variation in response to the present-day continent-ocean water exchange as well as its feedback to the sea level change is formulated.