Abstract: The high frequency scattering problems of electromagnetic fields scattered from electrically large scatterers are important and challenging. On the calculation of the reflected and diffracted wave fields, the high frequency methods could be classified into the current based method and the ray based method. In this paper, first, the author gives a review on the progress of the modern high frequency methods for solving the electromagnetic scattering problems. Next, due to the highly oscillatory property of the high frequency electromagnetic scattered fields, the author proposes the numerical steepest descent path method. Finally, the author comprehensively addresses the high frequency wave physics, including the high frequency critical point contributions, the Keller's cone, the shadow and reflection boundaries and the creeping wave fields.