A paper titled 'Quantised singularities in the electromagnetic field' by P.A.M. Dirac appeared in 1931 in the Proceedings of the Royal Society A. The paper concerned '[ · s] the reason for the existence of a smallest electric charge.' Dirac showed that the quantization of the electric charge follows from the existence of at least one free magnetic charge, finding 'a connection between the smallest electric charge and the smallest magnetic pole', a connection called since then the 'Dirac relation'. That seminal paper marked the opening of a new research field that has grown considerably since then. The search for magnetic monopoles in cosmic radiation encompasses many fields, from particle physics to astrophysics, from the extremely small to cosmology. This article is part of a discussion meeting issue 'Topological avatars of new physics'.
Keywords: Dirac relation; GUT theories; magnetic monopole.