Our theoretical proposal how to create an analogue Dirac monopole in a dilute Bose–Einstein condensate (BEC) [Pietilä and Möttönen, PRL 103, 030401 (2009)] has been the basis of series of beautiful experiments imaging for the first time in three-dimensional continuous fields the following topological structures: a Dirac monopole analogue, isolated monopole as a topological point defect, quantum knot as a realization of the Hopf fibration, and a skyrmion. More recently, we managed to experimentally observe the relaxation of the isolated monopole into a Dirac monopole accompanied by the spontaneous appearance of ending vortex lines, or nodal lines as coined by Dirac. Earlier decay dynamics of the isolated monopole showed the appearance of a half-quantum vortex ring, or an Alice ring. Such a ring has an intriguing, yet experimentally unobserved, property that any monopole passing through it has to change its sign. Thus, although the family of experimentally observed topological defects is complete on a general level, major new discoveries still await. To this end, we have theoretically considered knotted vortex cores characterized by different non-Abelian groups. Remarkably, we have very recently found that such a knotted structure may exist in a BEC and be topologically stable, save reasonable physically motivated assumptions. The experimental realization of these stable vortex knots remains one of the greatest challenges in the study of fundamental topological defects in physics.