  The performance characterization of communication systems assisted by large
reconfigurable intelligent surfaces (RISs) significantly depends on the adopted
models for the underlying channels. Under unrealistic channel models, the
system performance may be over- or under-estimated which yields inaccurate
conclusions for the system design. In this paper, we review five channel models
that are chosen to progressively improve the modeling accuracy for large RISs.
For each channel model, we highlight the underlying assumptions, its
advantages, and its limitations. We compare the system performance under the
aforementioned channel models using RIS configuration algorithms from the
literature and a new scalable algorithm proposed in this paper specifically for
the configuration of extremely large RISs.
