With the emergence of rotational seismology we have now access to new information about the interior of the Earth, in addition to the commonly measured translational motions. However, these motions are only partly described in the classical theory of elasticity and can be better accounted using more general theories, such as for instance the Cosserat brothers' theory (also called micropolar theory). It has the advantage to explicitly include rotational motions which brings a new elastic constant, the Cosserat couple modulus, that can help us to better describe the rheology of Earth's materials. Because this Cosserat couple modulus is not yet well understood, the application of this theory in seismology was until today quite limited. We present an unprecedented effort to link with solid physical basis the micropolar theory to seismology. We will first show how we have been recently able to evaluate the Cosserat couple modulus using Raman experiments. Then, we will show how we can better describe deformation with micropolar theory and the implications for our understanding of earthquake processes. Finally, we will show simulations of wave propagation in such medium and the effects on the wavefield. With the deployment of sufficient rotational seismometers we will soon get records of rotational motions to apply it.