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 magnetic monopoles necessitates exotic outgoing states, seemingly with fractional occupation numbers. I will first explain how we can make sense of these outgoing states in the modern language of generalised symmetries: They are created by operators living at the edge of a topological surface, and in turn correspond to states in a particular twisted Hilbert space. I will then apply this general formalism to the original case of interest, the Standard Model itself, where the resulting states turn out to carry fractionalised baryon and lepton numbers. I will finally discuss various other scenarios, including some that require non-invertible symmetry defects.