The challenge of explaining the origin of ultra-high-energy cosmic rays (UHECRs) is the need for a source class that can accelerate particles up to 100 EeV and that is abundant enough to produce a near-isotropic distribution in our local universe. Accretion shocks around clusters and filaments of the cosmic web are good sources because they can naturally explain the isotropic distribution at relatively low energies, while the most massive clusters create anisotropy at the highest energies. The biggest challenge for cluster shocks has always been the need for sufficient magnetic field amplification to allow efficient diffusive shock acceleration. We argue from simulations and observations that these shocks are strong enough for cosmic rays to generate enough magnetic turbulence to reaccelerate cosmic rays to the highest energies. The shocks around galaxy filaments contribute to the isotropic flux of cosmic rays at lower energies. This model is part of a hierarchical framework of shocks that explains the evolution of the cosmic-ray composition and spectral index. Electrons accelerated at accretion shocks could account for the observed radio synchrotron background below 10 GHz.