In this thesis, we investigate both theoretically and numerically the singularity formation and long time existence of three-dimensional vortex sheets. For the theoretical work, we divide it into two parts. In the first part, we study the early time singularity formation and the local form of the vortex sheet in the neighborhood of a singularity near the singularity time. We show that under a special set of coordinates, the three-dimensional vortex sheet can be viewed as a two-dimensional vortex sheet along certain space curves. As a result, the study of singularity formation of a three-dimensional vortex sheet can be related to that of the corresponding two-dimensional vortex sheet. And the singular behavior of these two problems is ver...