It’s been known since the work of Callan and Rubakov that a generic gauge theory harbours a riddle: the scattering of light fermions off heavy monopoles necessitates exotic outgoing states with fractional occupation numbers. I will first explain how we can finally make sense of these outgoing states in the modern language of generalised symmetries: They arise as states in a twisted Hilbert space, which is generated by operators at the edge of a topological surface. I will then apply this general formalism to the original case of interest, the Standard Model itself, which exhibits a number of new features. I will finally discuss various other scenarios, including some that require non-invertible symmetry defects.