Quantum electrodynamics predicts that in a strong electric field, electron–positron pairs are produced by the Schwinger process, which can be interpreted as quantum tunnelling through the Coulomb potential barrier. If magnetic monopoles exist, monopole–antimonopole pairs would be similarly produced in strong magnetic fields by the electromagnetic dual of this process. The production rate can be computed using semiclassical techniques without relying on perturbation theory, and therefore it can be done reliably in spite of the monopoles' strong coupling to the electromagnetic field. This article explains this phenomenon and discusses the bounds on monopole masses arising from the strongest magnetic fields in the universe, which are in neutron stars known as magnetars and in heavy ion... collision experiments such as lead–lead collisions carried out in November 2018 in the large Hadron collider at CERN. It will also discuss open theoretical questions affecting the calculation.This article is part of a discussion meeting issue ‘Topological avatars of new physics’.