In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow, surface diffusion flow, Willmore flow, etc., which arise from materials science, interface dynamics in multi-phase flows, biology membrane, computer graphics, geometry, etc. Different mathematical formulations and numerical methods for mean curvature flow are then discussed. In particular, an energy-stable semi-implicit parametric finite element method (PFEM) is presented in details. Then the PFEM is extended to surface diffusion flow. Finnally, sharp interface models and their PFEM approximations are presented for solid-state dewetting. This talk is based on joint works with Wei Jiang, Yan Wang, Quan Zhao, Yifei Li, David J. Srolovitz and Carl V. Thompson.