Cosmic rays can be accelerated to high energies by astrophysical objects embedded in clusters of galaxies or by shocks taking place in the intracluster medium. These cosmic rays are trapped within clusters, interacting with the gas and radiation permeating this environment, producing high-energy non-thermal messengers including neutrinos and gamma rays. These messengers can be observed either from individual clusters or as diffuse fluxes resulting from the whole population of these objects. While their fluxes depend on properties of the cosmic-ray emission, this contribution is guaranteed to exist, consequently constraining the parameter space available for other components that could generate them, such as some populations of astrophysical objects and the elusive dark matter. In this talk I will describe the propagation of high-energy cosmic rays in galaxy clusters considering a sample of these objects obtained from cosmological magnetohydrodynamical simulations of structure formation. I will then present estimates for the neutrino and gamma-ray fluxes from individual clusters, followed by estimates of the associated diffuse neutrino and gamma-ray fluxes. Finally, I will discuss these results within a broader astrophysical context, focusing on their importance for high-energy multi-messenger astronomy.