  The formulation of a complete theory of classical electromagnetism by Maxwell
is one of the milestones of science. The capacity of many-body systems to
provide emergent mini-universes with vacua quite distinct from the one we
inhabit was only recognised much later. Here, we provide an account of how
simple systems of localised spins manage to emulate Maxwell electromagnetism in
their low-energy behaviour. They are much less constrained by symmetry
considerations than the relativistically invariant electromagnetic vacuum, as
their substrate provides a non-relativistic background with even translational
invariance broken. They can exhibit rich behaviour not encountered in
conventional electromagnetism. This includes the existence of magnetic monopole
excitations arising from fractionalisation of magnetic dipoles; as well as the
capacity of disorder, by generating defects on the lattice scale, to produce
novel physics, as exemplified by topological spin glassiness or random Coulomb
magnetism.
