We present a novel multi-trace surface integral equation (SIE) method for solving multi-scale and complex electromagnetic problems. There are three major technical ingredients in the proposed SIE formulation: a. A discontinuous Galerkin integral equation method, which makes it possible to solve surface integral equations without any interelement continuity condition; b. A multi-trace surface integral equation domain decomposition method (SIE-DDM) to account for multi-scale composite targets; and, c. A optimized second order transmission condition to enforce currents continuities across domain interfaces. It further improves the convergence of SIE-DDM for electrically large problems. The strength of the proposed method is illustrated by means of challenge real-world applications.