A central question in geometric flows is to understand the formation of singularities. In this talk, I will focus on mean curvature flow, the negative gradient flow of area functional, and explain how the local dynamics influence the shape of the flow and its singular set near a cylindrical singularity, as well as how the topology of the flow changes after passing through such a singularity with generic dynamics. This talk is based on the joint works with Ao Sun and Jinxin Xue.