We will consider the water waves problem for 2D and 3D  incompressible, irrotational, inviscid fluid flows subject to both gravity and surface tension. The PDE is dispersive, quasilinear and nonlocal. The questions on local existence and uniqueness in the lowest regularity spaces are still in progress. We will discuss our results on a blow-up criterion in terms of the Lipschitz norm of the velocity; nonlinear Strichartz estimates for rough solutions; and their application in estabishing a local well-posedness theory for non-Lipschitz initial velocity.