Compton scattering on light nuclei ($A=2,3$) has emerged as an effective avenue to search for signatures of neutron polarizabilities, both spin--independent and spin--dependent ones. In this discussion I will focus on the theoretical aspect of Compton scattering on light nuclei; giving first a brief overview and therafter concentrating on our Compton scattering calculations based on Chiral effective theory at energies of the order of pion mass. These elastic $gamma$d and $gamma$He-3 calculations include nucleons, pions as the basic degrees of freedom. I will also discuss $gamma$d results where the $Delta$-isobar has been included explicitly. Our results on unpolarized and polarization observables suggest that a combination of experiments and further theoretical efforts will provide an extraction of the neutron polarizabilities.
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