In this dissertation, we discussed the new development of scattering amplitudes in gauge and gravities theories. The LHC era requires the new development of scattering amplitude beyond the traditional Feynman diagram approach. We reviewed the new scattering amplitude methods, inspired by string theory, analyticity and supersymmetry. With these new methods, we [37][54] proved (1) the color/kinematics equivalence in Bern-Carrasco-Johansson (BCJ) recursive identity from the viewpoint of heterotic string theory and (2) the quadratic identities for Yang-Mills theory via the Kawai-Lewellen-Tye (KLT) relation. Both identities simplify the Yang-Mills amplitude calculation and illustrate deep structures in gauge and gravity theories.