  While astrophysical and cosmological probes provide a remarkably precise and
consistent picture of the quantity and general properties of dark matter, its
fundamental nature remains one of the most significant open questions in
physics. Obtaining a more comprehensive understanding of dark matter within the
next decade will require overcoming a number of theoretical challenges: the
groundwork for these strides is being laid now, yet much remains to be done.
Chief among the upcoming challenges is establishing the theoretical foundation
needed to harness the full potential of new observables in the astrophysical
and cosmological domains, spanning the early Universe to the inner portions of
galaxies and the stars therein. Identifying the nature of dark matter will also
entail repurposing and implementing a wide range of theoretical techniques from
outside the typical toolkit of astrophysics, ranging from effective field
theory to the dramatically evolving world of machine learning and
artificial-intelligence-based statistical inference. Through this work, the
theory frontier will be at the heart of dark matter discoveries in the upcoming
decade.
