After the publication of Einstein's theory of General Relativity in 1915, many predictions have been confirmed in the latest one century, recently culminating at the observations of gravitational waves emitted during the merging of binary black holes by LIGO and VIRGO collaborations and the first obtained image of a black hole by Event Horizon Telescope. Black holes are one of the fundamental predictions in the theory of General Relativity, and the ones of most interests are the Kerr black hole spacetimes, the metrics of which describe a family of rotating, stationary, axisymmetric, asymptotically flat solutions to vacuum Einstein equations. In this talk, I will present my recent results towards the fully nonlinear stability conjecture of the Kerr solutions.
