In the first of the talk I will discuss the phenomenology of cosmic-ray diffusion in the Galaxy and the associated gamma-ray and neutrino emission. The aim is to understand how the combined study of local cosmic-ray spectra and diffuse emissions can help to unveil anomalies that may point towards either non-standard propagation scenarios (and new astrophysical phenomena in general), or new physics (for instance, particle dark matter annihilation/decay). I will then move to the cosmological settings, and explore - mainly in the context of CMB studies - how dark matter can leave an observable imprint focusing in particular on the WIMP and primordial black hole case study, and again discussing the interplay with astrophysical issues.