In the simple exclusion process on a finite segment, a particle is allowed to move to the right at rate $p$ and to the left at rate $q$, provided that the selected site is empty. In joint work with Nina Gantert and Domink Schmid, we study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on $p,q$ as well as on the entering and exiting rates, and show that the process exhibits pre-cutoff and in some special cases even cutoff.