This white paper discusses the current landscape and prospects for experiments sensitive to particle dark matter processes producing photons and cosmic rays. Much of the γ-ray sky remains unexplored on a level of sensitivity that would enable the discovery of a dark matter signal. Currently operating GeV-TeV observatories, such as Fermi-LAT, atmospheric Cherenkov telescopes, and water Cherenkov detector arrays continue to target several promising dark matter-rich environments within and beyond the Galaxy. Soon, several new experiments will continue to explore, with increased sensitivity, especially extended targets in the sky. This paper reviews the several near-term and longer-term plans for γray observatories, from MeV energies up to hundreds of TeV. Similarly, the X-ray sky has been and continues to be monitored by decade-old observatories. Upcoming telescopes will further bolster searches and allow new discovery space for lines from, e.g., sterile neutrinos and axion-photon conversion.Furthermore, this overview discusses currently operating cosmic-ray probes and the landscape of future experiments that will clarify existing persistent anomalies in cosmic radiation and spearhead possible new discoveries.Finally, the article closes with a discussion of necessary cross section measurements that need to be conducted at colliders to reduce substantial uncertainties in interpreting photon and cosmic-ray measurements in space.Snowmass2021 Cosmic Frontier: The landscape of cosmic-ray and high-energy photon probes of particle dark matter Snowmass2021 Cosmic Frontier: The landscape of cosmic-ray and high-energy photon probes of particle dark matter