Future galaxy surveys are aiming to constrain the neutrino mass from the suppression of the matter power spectrum due to neutrino free-streaming. This requires to account for non-linearities in the evolution of the matter overdensity with an accuracy at the (sub-)percent level. In this talk I discuss recent progress on the perturbative approach to structure formation in the presence of massive neutrinos, with an emphasis on certain conceptual challenges. Finally, I present an effective approach to obtain limits from BOSS Lyman alpha data while marginalizing over uncertainties due to baryonic and non-linear physics.