  In this sketch, I focus on Physics and formalism behind dynamical
polarisabilities, a new tool to test and interpret quantitative predictions
about the low-energy degrees of freedom inside the nucleon from the multipoles
of Compton scattering for photon energies below 300 MeV. A way to extract them
from double-polarised precision experiments is sketched. Predictions from
Chiral Effective Field Theory, both on the proton and on the neutron, serve as
guideline for forthcoming experiments. Special interest is put on the r\^ole of
the nucleon spin-polarisabilities. For details and a complete list of
references, consult Refs. [1,2,3].
