
The origin and nature of the ultra-high-energy cosmic rays (UHECRs) is one of the main challenges astroparticle physics. I will discuss the difficulties in modelling the propagation of ultra-high-energy cosmic rays, given our limited knowledge of the extragalactic background light, photonuclear interactions, and cosmic magnetic fields. Particularly, I will focus on the influence of magnetic fields on the propagation, and discuss the prospects for UHECR astronomy in light of results of numerical simulations of cosmic ray propagation in the magnetised cosmic web.