These notes summarize the lectures about “Cosmic-ray propagation in extragalactic space and secondary messengers”, focusing in particular on the interactions of cosmic-ray particles with the background photons in the Universe, including nuclear species heavier than hydrogen, and on the analytical computation of the expected cosmic-ray fluxes at Earth. The lectures were held at the Course 208 of the International School of Physics “Enrico Fermi” on Foundations of Cosmic-Ray Astrophysics, in Varenna (Como, Italy) from June 23rd to June 29th, 2022. These notes are complementary to the content of the lectures held by Pasquale Dario Serpico at the same school.