The free-boundary Euler equations describe the motion of perfect fluids with free surfaces or with moving material interfaces. The nonlinear a priori estimates for this system rely heavily on the geometric structures present in these equations, and it turns out that finding approximations which do not destroy this structure, and for which existence and uniqueness can be proven, is somewhat difficult. I will discuss the geometric a priori estimates for Euler, as well as a new method for well-posedness that relies on a "convolution by horizontal layers" smoothing operator as well as artificial viscosity in the case of surface tension. No irrotationality assumptions are made so that we can study general fluid motion problems, and in particular, the effect of vorticity on boundary shape, and vice versa.