Abstract: We will present a new result studying the global dynamics of apparent horizon based on null foliations. A new null comparison principle is also proposed to prove the achronality of the apparent horizon. And it applies to three typical scenarios arising from gravitational collapse. If time permits, I will also discuss about a new angular momentum memory effect of gravitational waves along null infinity based on recent progress in proving stability of Minkowski spacetime with minimal decays and nonlinear stability of Kerr black holes with small angular momentum.