I will review the recent progress, including my own contribution, in addressing the Kerr Stability Conjecture (克尔时空稳定性猜想）and the Strong Cosmic Censorship Hypothesis (强宇宙监督假设)，both of which are among the most fundamental questions in the theory of General Relativity. If time permits, I will also describe my future projects in making further advance in these two conjectures.
