What is the birational classification of (smooth projective) rationally connected 3-folds (over algebraically closed fields of characteristic $0$ or even $\mathbf{C}$, if $\mathrm{char}(k) = p > 0$, one should perhaps better ask for separably rationally connected 3-folds).
There is perhaps an article of Iskovskikh, but I do not have access to MathSciNet at the moment.