I will describe some aspects of the proof of the nonlinear stability of subextremal Kerr black holes, as solutions of the Einstein vacuum equations, in arXiv:2606.28253. I will emphasize the role of mode stability, the choice of gauge, and some basic aspects of the nonlinear analysis which is based on a general-purpose framework (arXiv:2606.28008) for proving decay of waves on dynamical black hole spacetimes.