I review the theory side of the synergetic international effort of experimentalists and theorists in Compton scattering on one- and few-nucleon systems. It is an excellent opportunity to probe the symmetries and strengths of nucleonic and nuclear interactions and relate to lattice-QCD computations of fundamental hadronic properties. The polarizabilities parametrize the stiffness of charge distributions against deformations. In particular, their spin component parametrizes the stiffness of the spin in external electromagnetic fields (nucleonic Faraday effect) and probe the spin-dependent component of the pion-nucleon interaction. Using the statistical methods of Bayesian analysis and experimental design, we identify kinematics and observables with the likely biggest impact.
