Extragalactic propagation of ultrahigh energy cosmic-rays

45 pages, 16 figures; Cosmic Rays Topical IssueInternational audienceIn this paper we review the extragalactic propagation of ultrahigh energy cosmic-rays (UHECR). We present the different energy loss processes of protons and nuclei, and their expected influence on energy evolution of the UHECR spectrum and composition. We discuss the possible implications of the recent composition analyses provided by the Pierre Auger Observatory. The influence of extragalactic magnetic fields and possible departures from the rectilinear case are also mentioned as well as the production of secondary cosmogenic neutrinos and photons and the constraints their observation would imply for the UHECRs origin. Finally, we conclude by briefly discussing the relevance of a multi messenger approach for solving the mystery of UHECRs