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Published online by Cambridge University Press: 27 February 2023
While predominantly dipolar, large-scale magnetic fields are usually assumed in most studies involving neutron stars, there are multiple observational, theoretical hints and numerical simulations highlightening the importance of non-dipolar components. I review here the most important observational facts and numerical studies pointing towards the existence of magnetospheric currents and internal small-scale structures, arising from multipoles of poloidal and toroidal fields. This holds for all neutron star stages: at birth, during their lifetime and after a merger.