Non-standard interactions (NSI) between neutrinos and electrons modify the decoupling of neutrinos from the cosmic plasma. These interactions have two effects on the overall picture: (i) they alter neutrino oscillations though matter effects and (ii) they modify the
scattering and annihilation processes involving neutrinos and electrons and positrons. We address the role of different NSI in the decoupling process and study how they impact the determination of the effective number of neutrinos, $N_{\rm eff}$ . We examine the existing degeneracies between NSI parameters and we compare the expected sensitivity from future cosmological surveys with
the current limits from terrestrial experiments. We also comment on the apparent phenomenological similarities between NSI and some scenarios where Lorentz invariance is not preserved, and we discuss the robustness of the NSI limits derived from cosmological observations.