The borders between galaxies and the almost empty intergalactic medium are ill-defined regions where gas struggles to form stars. The proceedings of IAU Symposium 321 summarize our current understanding of the rarefied universe and prepare for the optimal exploitation of upcoming astronomical instruments. They discuss the most recent advances in the study of the stellar, dust and gas content of galaxy outskirts, going from resolved stellar populations in the Milky Way and in the Local Group to the study of high-redshift systems. Such a broad approach, both in terms of galaxy components and evolutionary epochs, is necessary to take full advantage of the recent discoveries made by facilities at all wavelengths, to deepen our knowledge of the assembly and evolution of these elusive regions and to establish their role within the evolution of galaxies as a whole and their interactions with the surrounding intergalactic medium.