Observation of the variations in the Earth's rotation at time scales ranging from subdiurnal to multidecadal allows us to learn about its deep interior structure. We review all three types of motion of the Earth's rotation axis: polar motion (PM), length of day variations (Delta LOD) and nutations, with particular attention to how the combination of geodetic, magnetic and gravity observations provides insight into the dynamics of the liquid core, including its interactions with the mantle. Models of the Earth's PM are able to explain most of the observed signal with the exception of the so-called Markowitz wobble. In addition, whereas the quasi-six year oscillations (SYO) observed in both Delta LOD and PM can be explained as the result of Atmosphere, Oceans and Hydrosphere Forcing (AOH) for PM, this is not true for Delta LOD where the subtraction of the AOH only makes the signal more visible. This points to a missing-possibly common-interpretation related to deep interior dynamics, the latter being also the most likely explanation of other oscillations in Delta LOD on interannual timescales. Deep Earth's structure and dynamics also have an impact on the nutations reflected in the values of the Basic Earth Parameters (BEP). We give a brief review of recent works aiming to independently evaluate the BEP and their implications for the study of deep interior dynamics.
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