Pristine collisionless shocks were recently detected around galaxy clusters: island universes feeding at the cosmic-web nodes, the largest objects ever to virialize. Although collisionless shocks were anticipated in the 1950s, a self-consistent model for these natural particle accelerators, which boost charged particles to ultra-relativistic cosmic rays, is still unavailable. Galaxy-cluster observations regularly challenge theory, with no self-consistent models for their structure, apparent cooling stability, and unexpected spiral dynamics. Challenges and new hints pertaining to both collisionless-shock and galaxy-cluster physics will be outlined.