  We are at the dawn of a data-driven era in astrophysics and cosmology. A
large number of ongoing and forthcoming experiments combined with an
increasingly open approach to data availability offer great potential in
unlocking some of the deepest mysteries of the Universe. Among these is
understanding the nature of dark matter (DM)---one of the major unsolved
problems in particle physics. Characterizing DM through its astrophysical
signatures will require a robust understanding of its distribution in the sky
and the use of novel statistical methods.
  The first part of this thesis describes the implementation of a novel
statistical technique which leverages the "clumpiness" of photons originating
from point sources (PSs) to derive the properties of PS populations hidden in
astrophysical datasets. This is applied to data from the Fermi satellite at
high latitudes ($|b| > 30$\deg) to characterize the contribution of PSs of
extragalactic origin. We find that the majority of extragalactic gamma-ray
emission can be ascribed to unresolved PSs having properties consistent with
known sources such as active galactic nuclei. This leaves considerably less
room for significant dark matter contribution.
  The second part of this thesis poses the question: "what is the best way to
look for annihilating dark matter in extragalactic sources?" and attempts to
answer it by constructing a pipeline to robustly map out the distribution of
dark matter outside the Milky Way using galaxy group catalogs. This framework
is then applied to Fermi data and existing group catalogs to search for
annihilating dark matter in extragalactic galaxies and clusters.
