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. 

In this talk, I will review the progress made in the last three decades towards such an accurate prediction, and present results including for the first time the full collision term which accounts for neutrino mixing. A particular focus will be placed on the physical effect of neutrino oscillations, which allows for an approximate numerical scheme of striking accuracy.