Cosmic-Ray induced diffuse emissions from the Milky Way and Local Group galaxies

Cosmic rays fill up the entire volume of galaxies, providing an important source of heating and ionisation of the interstellar medium, and may play a significant role in the regulation of star formation and galactic evolution. Diffuse emissions from radio to high-energy γ-rays (>100 MeV) arising from various interactions between cosmic rays and the interstellar medium, interstellar radiation field, and magnetic field, are currently the best way to trace the intensities and spectra of cosmic rays in the Milky Way and other galaxies. In this contribution, I describe our recent work to model the full spectral energy distribution of galaxies like the Milky Way from radio to γ-ray energies. The application to other galaxies, in particular the Magellanic Clouds and M31 that are now resolved in high-energy γ-rays by the Fermi-LAT, is also discussed.