  The study of comets affords a unique window into the birth, infancy, and
subsequent history of the solar system. There is strong evidence that comets
incorporated pristine interstellar material as well as processed nebular
matter, providing insights into the composition and prevailing conditions over
wide swaths of the solar nebula at the time of planet formation. Dynamically
new Oort cloud comets harbor primitive ices that have been stored thousands of
astronomical units from the Sun and have suffered minimal thermal or radiative
processing since their emplacement ~4.5 Gyr ago. Periodic, more dynamically
evolved comets such as the Halley-type and Jupiter-family comets reveal the
effects of lives spent over a range of heliocentric distances, including
perihelion passages into the very inner solar system. Systematically
characterizing the information imprinted in the native ice compositions of
these objects is critical to understanding the formation and evolution of the
solar system, the presence of organic matter and water on the terrestrial
planets, the chemistry present in protoplanetary disks around other stars, and
the nature of interstellar interlopers such as 2I/Borisov. Although comet
rendezvous and sample return missions can provide remarkable insights into the
properties of a few short-period comets, the on-sky capacity necessary to
perform population-level comet studies while simultaneously remaining sensitive
to the paradigm-challenging science that individual comets can reveal can only
be provided by remote sensing observations. Here we report the state-of-the-art
in ground- and space-based remote sensing of cometary volatiles, review the
remarkable progress of the previous decade, articulate the pressing questions
that ground- and space-based work will address over the next ten years, and
advocate for the technology and resources necessary to realize these
aspirations.
