In this talk I will present a recent work in collaboration with Jiajiang Liao and Ping Zhang regarding the controllability of the 3D Navier-Stokes equation in a smooth bounded domain, with a control on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the remaining, uncontrolled, part of the boundary. We prove that for any positive time, for any smooth initial velocity field, there exist a control such that the corresponding unique smooth solution vanishes at the given time. This extends a previous result in collaboration with Jean-Michel Coron and Frédéric Marbach where we proved that for any positive time, for any finite energy initial data, there exist some controls and some Leray weak solutions which vanish at the given time. I will also present another controllability result which concerns the Lagrangian point of view: for two smooth contractible sets of fluid particles, surrounding the same volume, for any given smooth initial velocity field and any positive time interval, we prove that one can find some controls such that the corresponding solution makes the first of the two sets approximately reach the second one, while staying in the domain in the meantime.