Superfluidity in dilute neutron matter has important consequences on neutron star properties such as cooling and glitches. However, the theoretical predictions for the superfluid critical temperature and the pairing gap have still very large uncertainties, especially if one goes beyond the simplest BCS approximation. In this talk, I will first discuss the contribution of correlated pairs to the density which lowers the critical temperature. This effect is described in the framework of the NoziÃ¨res-Schmitt-Rink theory and is well known from ultracold atoms in the BCS-BEC crossover. Then I will discuss recent results for corrections from screening of the pairing interaction due to particle-hole effects. In the weak coupling limit, this is known as the Gor'kov-Melik-Barkhudarov correction, but in neutron matter it is necessary to include the RPA in addition to the uncorrelated particle-hole bubble. It turns out that the screening may turn into anti-screening at densities which are still far below nuclear saturation density.