For over a century, both experimentalists and theorists have been fascinated by the possible existence of magnetic monopoles. Theoretical analysis of monopole interactions is difficult due to the inherently strongly coupled nature of charge-monopole interactions. Several apparent paradoxes in monopole physics have attracted attention for decades yet remain unresolved. In this talk, I will begin by reviewing aspects of theories with both electric and magnetic states. Some of the asymptotic states of these theories carry additional angular momentum and as a result do not factorize as products of single particles. To account for this angular momentum, I will discuss a generalization of the Wigner classification for multi-particle states. Making use of this new formalism, I will use on-shell methods to constrain electric-magnetic scattering processes without appealing to the underlying dynamics of the theory. In particular, I will reproduce known results for 2->2 fermion-monopole scattering in a manifestly relativistic fashion. I will conclude with comments on possible applications of our formalism.