Abstract: In the first part of the talk, I will argue that an asymptotic multi-particle state built as a product of one-particle states is not fully general. In addition, I will show that the more general asymptotic multi-particle state carries extra quantum number, pairwise-helicity, on top of the regular labels such as momentum and spin/helicity of each particle. In the second part of the talk, the S-matrix for the scattering of electrically and magnetically charged particles will be considered. After discussing several non-conventional properties of the electric-magnetic S-matrix, including the extra pairwise-helicity carried by the electric-magnetic asymptotic state and the associated crossing symmetry violation, modern on-shell scattering amplitude method will be motivated as a way to construct the electric-magnetic S-matrix. Pairwise spinor-helicity variables as additional building blocks for the electric-magnetic S-matrix will then be introduced. Discussion on the general three-point amplitudes and resulting generalized spin-helicity selection rules comes next. Finally, I describe the partial-wave decomposition of the 2 to 2 electric-magnetic S-matrix, showing that the well-known results based on QM computations are reproduced with a small input about the phase shift. In particular, the helicity-flip in the lowest partial wave is shown to be a simple consequence of a generalized spin-helicity selection rule. Furthermore, the full angular dependence for the higher partial waves is shown to agree with QM results. Our work represents a remarkable success of on-shell methods for non-perturbative physics, especially when the Lagrangian description fails.