Abstract: In this presentation, We will study a new method different from default Feynman's method for calculating scattering amplitudes. This method is based on amplitudes with on-shell elements. We Start using Spinor Formalism for calculating tree-level and then M.H.V. amplitudes in Yung-Mills theory. The main step will be the Introduction of recursion relations for tree-level amplitudes, specially a powerful method; BCFW. Then we study on-shell method and recursion relation in N=4 Super Yung-Mills theory. Next we try to calculate loop-level amplitudes using on-shell methods. And finally, We will discuss the recent achievements in this field; Grassmannia as a replacement for Feynman diagrams in Twistor space.