  Satellite communications industry is currently going through a rapid and
profound transformation to adapt to the recent innovations and developments in
the realm of non-geostationary orbit (NGSO) satellites. The growing popularity
of NGSO systems, with cheap manufacturing and launching costs, has set to
revolutionize the internet market. In this context, accurate channel
characterization is crucial for the performance optimization and designing
efficient NGSO communications, especially considering the dynamic propagation
environment. While the Third Generation Partnership Project (3GPP) has provided
some guidelines in Release 15, we observed certain divergence on the channel
models considered in the literature, each with different assumptions and
peculiarities. This paper provides an extensive review of the existing methods
proposed for NGSO channel modeling that consider different orbits, frequency
bands, user equipment, use-case and scenario peculiarities. The provided review
discusses the channel modeling efforts from a contemporary perspective through
trade-off analyses, classifications, and highlighting their advantages and
pitfalls. The main goal is to provide a comprehensive overview of NGSO channel
models to facilitate the selection of the most appropriate channel based on the
scenario requirements to be evaluated and/or analysed.
