  We review the long standing problem of superfluid pairing in pure neutron
matter. For the $s$-wave pairing, we summarize the state of the art of
many-body approaches including different $nn$ interactions, medium
polarization, short-range correlations and BCS-BEC crossover effects, and
compare them with quantum Monte Carlo results at low-densities. We also address
pairing in the $p$-wave, which appears at higher densities and hence has large
uncertainties due to the poorly constrained interactions, medium effects and
many-body forces.
