  The epoch of Cosmic Dawn, when the first stars and galaxies were born, is
widely considered the final frontier of observational cosmology today. Mapping
the period between Cosmic Dawn and the present-day provides access to more than
90% of the baryonic (normal) matter in the Universe, and unlocks several
thousand times more Fourier modes of information than available in today's
cosmological surveys. We review the progress in modelling baryonic gas
observations as tracers of the cosmological large-scale structure from Cosmic
Dawn to the present day. We illustrate how the description of dark matter
haloes can be extended to describe baryonic gas abundances and clustering. This
innovative approach allows us to fully utilize our current knowledge of
astrophysics to constrain cosmological parameters from future observations.
Combined with the information content of multi-messenger probes, this will also
elucidate the properties of the first supermassive black holes at Cosmic Dawn.
We present a host of fascinating implications for constraining physics beyond
the $\Lambda$CDM model, including tests of the theories of inflation and the
cosmological principle, the effects of non-standard dark matter, and possible
deviations from Einstein's general relativity on the largest scales.
