Snowmass2021 Cosmic Frontier White Paper: Puzzling Excesses in Dark Matter Searches and How to Resolve Them

Intriguing signals with excesses over expected backgrounds have been observed in many astrophysical and terrestrial settings, which could potentially have a dark matter origin. Astrophysical excesses include the Galactic Center GeV gamma-ray excess detected by the Fermi Gamma-Ray Space Telescope, the AMS antiproton and positron excesses, and the 511 and 3.5 keV X-ray lines. Direct detection excesses include the DAMA/LIBRA annual modulation signal, the XENON1T excess, and low-threshold excesses in solid state detectors. We discuss avenues to resolve these excesses, with actions the field can take over the next several years.