In the primordial Universe, neutrino decoupling occurs only slightly before electron-positron annihilations. This leads to an increased neutrino energy density with order 1% spectral distortions compared to the standard instantaneous decoupling approximation. A precise calculation of neutrino evolution is needed to assess its consequences on BBN, structure formation or on the CMB, and requires to take into account multiple effects such as neutrino oscillations, which represents a genuine numerical challenge.