Galaxy clusters continuously accrete gas and galaxies from filaments of the cosmic web. As the cold gas which is accreted falls into the hot intracluster medium, it gives rise to shocks at the outskirts of the cluster, which could accelerate cosmic rays through the diffusive shock acceleration mechanism. Large scale radio halos and radio relics, which are expected to be due to synchrotron emission from relativistic electrons, show that clusters do host high energy particles. Studies have found that shocks in clusters can accelerate iron nuclei to 10 eV, which is nearly as much as the most energetic cosmic rays observed by the Pierre Auger Observatory. However, if clusters do accelerate protons or nuclei to such high energies, they should also produce gamma ray emission due to the interaction of the high-energy particles with the intracluster medium. This gamma ray emission has not yet been observed, which is difficult to explain.