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In this proceedings article we present a selected set of our lattice results
regarding the effect that background electromagnetic fields have on the
topology of QCD. In particular, we report on the lattice spacing-dependence of
the axion-photon coupling as well as on the response of the topological
susceptibility to strong magnetic fields at nonzero temperatures. We
demonstrate that the ratio of topological susceptibilities at finite to zero
magnetic field has a well behaved continuum limit at low temperatures using a
reweighting technique. Moreover, we study the scaling of the axion-photon
coupling towards the continuum limit and show that it is less severely affected
by discretisation effects.
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