[en] The nature of dark matter is one of the key outstanding problems in both particle and astrophysics. If dark matter decays or annihilates into electrons and positrons, it can affect diffuse radiation backgrounds observed in astrophysics. In this thesis, we propose a new, more general analysis of constraints on dark matter models. For any decaying dark matter model, constraints on mass and lifetime can be obtained by folding the specific dark matter decay spectrum with a response function. We derive these response functions from full-sky radio surveys and Fermi-LAT gamma-ray observations as well as from the local positron fluxes measured by the PAMELA satellite experiment and apply them to place constraints on some specific dark matter decay models. We also discuss the influence of astrophysical uncertainties on the response function, such as the uncertainties from propagation models and from the spatial distribution of the dark matter. Moreover, an anisotropy analysis of full-sky emission gamma-ray and radio maps is performed to identify possible signatures of annihilating dark matter. We calculate angular power spectra of the cosmological background of synchrotron emission from dark matter annihilations into electron positron pairs. We compare the power spectra with the anisotropy of astrophysical and cosmological radio backgrounds, from normal galaxies, radio-galaxies, galaxy cluster accretion shocks, the cosmic microwave background and Galactic foregrounds. In addition, we develop a numerical tool to compute gamma-ray emission from such electrons and positrons diffusing in the smooth host halo and in substructure halos with masses down to 10^-6M_sun. We show that, unlike the total gamma-ray angular power spectrum observed by Fermi-LAT, the angular power spectrum from the inverse Compton scattering is exponentially suppressed below an angular scale determined by the diffusion length of electrons and positrons. (orig.)