The celestial Earth's orientation is required for many applications in fundamental astronomy and geodesy; it is currently determined with sub-milliarcsecond accuracy by astro-geodetic observations. Models for that orientation rely on solutions for the rotation of a rigid Earth model and on the geophysical representation of non-rigid Earth effects. Important IAU 2000/2006 resolutions on reference systems have been passed (and endorsed by the IUGG) that recommend a new paradigm and high accuracy models to be used in the transformation from terrestrial to celestial systems. This paper reviews the consequences of these resolutions on the adopted Earth orientation parameters, IAU precession-nutation models and associated nomenclature. It summarizes the fundamental aspects of the current IAU precession-nutation models and reports on the consideration of General Relativity (GR) in the solutions. This shows that the current definitions and nomenclature for Earth's rotation are compliant with GR and that the IAU precession-nutation is compliant with the IAU 2000 definition of the geocentric celestial reference system in the GR framework; however, the underlying Earth's rotation models basically are Newtonian.