Chiral Effective Field Theory is for photon energies up to 200 MeV the tool to accurately determine the polarisabilities of the neutron from deuteron Compton scattering. A multipole analysis reveals that dispersive effects from an explicit Delta(1232) prove in particular indispensable to understand the data at 95 MeV measured at SAL. Simple power-counting arguments derived from nuclear phenomenology lead to the correct Thomson limit and gauge invariance. At next-to-leading order, the static scalar dipole polarisabilities are extracted as identical for proton and neutron within the error-bar of available data: \alpha^n=11.6\pm1.5_stat\pm0.6_Baldin, \beta^n=3.6\mp1.5_stat\pm0.6_Baldin for the neutron, in units of 10^-4 fm^3, compared to \alpha^p=11.0\pm1.4_stat\pm0.4_Baldin, \beta}^p=2.8\mp1.4_stat\pm0.4_Baldin for the proton in the same framework. New experiments e.g. at MAXlab (Lund) will improve the statistical error-bar.

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