The study of high-energy emission from galaxies provides us rich information about acceleration and propagation of cosmic rays, their impact on the galaxy evolution, and the nature of high-energy cosmic particle backgrounds. 

 We first discuss the gamma-ray emission from the whole galaxy, which originates from cosmic rays interacting with interstellar medium, focusing on the importance of galaxies across cosmic time for the cosmic background flux of high-energy gamma-ray and neutrino. We present theoretical modelling of gamma-ray and neutrino production in star-forming galaxies, which agrees well with observations of galaxies from dwarfs to starbursts. We incorporate this to the model of cosmological galaxy formation and predict that galaxies produce about 20% of the isotropic gamma-ray background unresolved by Fermi and at most 22% of the IceCube neutrinos. 

 We then discuss the emission from discrete sources in the galaxy, with particular focus on the extended TeV haloes around pulsars, which is newly identified class of gamma-ray emitters. We assess the importance of TeV haloes based on pulsar population synthesis models, using Geminga as a standard candle. We discuss their implications for TeV surveys and the modelling of pulsar evolution.