Over different timescales, the Earth materials deform in various ways. It is well-known that the Earth mantle exhibits a quasi-elastic behaviour in the seismic frequency band and behaves like a viscous fluid at very large periods, yet more complex behaviours are observed, including viscoelastic deformations. The study of these deformations is the object of rheology, which is a key to properly understand many geodynamic processes.
After a brief introduction to rheology, I will give an overview of the anelastic effects in geophysics. Then, we will focus on two topics: (1) the influence of anelasticity on the rotation of the Earth and how studying the latter can provide some insight into the mantle rheology, and (2) the Glacial Isostatic Adjustment, one of the very few geophysical phenomena we can directly observe to estimate the viscosity of the Earth mantle.