We consider the free boundary problem for a 2D and 3D fluid filtered in porous media, which is known as the one-phase Muskat problem. We show that if the initial free boundary is the graph of a periodic Lipschitz function, then there exists a unique global Lipschitz strong solution. The proof of the uniqueness relies on a new pointwise $C^{1,\alpha}$ estimate near the boundary for harmonic functions. This is based on joint work with Francisco Gancedo (Universidad de Sevilla, Spain) and Huy Q. Nguyen (University of Maryland, USA).