  We present the first $ab$-$initio$ study of superconductivity in NbTi, the
workhorse for many applications. Despite its apparent simplicity, NbTi turns
out to be a major challenge for computational superconductivity. In fact,
anharmonic effects are crucial to obtain dynamically stable phonons for the
ordered bcc phase, unstable at the harmonic level, and beyond-Morel Anderson
effects in the Coulomb interaction reduce the Tc by more than 20%. Lattice
disorder causes an additional large discrepancy in $T_c$ compared to
experiment. Our results imply that a quantitative description of
technologically-relevant superconductors requires methodological developments
beyond the current standards.
