The Dirac equation is a wave-type relativistic equation describes the spin-1/2 particles.  In this talk, we will first introduce the vector field methods and the results about classical wave equations. Then we talk about the Dirac equation in Minkowski spacetime. In a geometric viewpoint, we will find spinor fields satisfy the Dirac equation will enjoy the so-called peeling properties. It means the null components of the solution will decay in different rates along  null directions. Based on this decay mechanism, we will have a new insight to the spinor null structure which contribute to prove a small data global existence result especially for some important nonlinear Dirac models.