  Free core nutation (FCN) is the main factor that limits the accuracy of the
modeling of the motion of Earth's rotational axis in the celestial coordinate
system. Several FCN models have been proposed. A comparative analysis is made
of the known models including the model proposed by the author. The use of the
FCN model is shown to substantially increase the accuracy of the modeling of
Earth's rotation. Furthermore, the FCN component extracted from the observed
motion of Earth's rotational axis is an important source for the study of the
shape and rotation of the Earth's core. A comparison of different FCN models
has shown that the proposed model is better than other models if used to
extract the geophysical signal (the amplitude and phase of FCN) from
observational data.
