  Recent years have seen increased theoretical and experimental effort towards
the first-ever detection of cosmic-ray antideuterons, in particular as an
indirect signature of dark matter annihilation or decay. In contrast to
indirect dark matter searches using positrons, antiprotons, or gamma-rays,
which suffer from relatively high and uncertain astrophysical backgrounds,
searches with antideuterons benefit from very suppressed conventional
backgrounds, offering a potential breakthrough in unexplored phase space for
dark matter. This article is based on the first dedicated cosmic-ray
antideuteron workshop, which was held at UCLA in June 2014. It reviews broad
classes of dark matter candidates that result in detectable cosmic-ray
antideuteron fluxes, as well as the status and prospects of current
experimental searches. The coalescence model of antideuteron production and the
influence of antideuteron measurements at particle colliders are discussed.
This is followed by a review of the modeling of antideuteron propagation
through the magnetic fields, plasma currents, and molecular material of our
Galaxy, the solar system, the Earth's geomagnetic field, and the atmosphere.
Finally, the three ongoing or planned experiments that are sensitive to
cosmic-ray antideuterons, BESS, AMS-02, and GAPS, are detailed. As cosmic-ray
antideuteron detection is a rare event search, multiple experiments with
orthogonal techniques and backgrounds are essential. Many theoretical and
experimental groups have contributed to these studies over the last decade,
this review aims to provide the first coherent discussion of the relevant dark
matter theories that antideuterons probe, the challenges to predictions and
interpretations of antideuteron signals, and the experimental efforts toward
cosmic antideuteron detection.
