The 100th birthday of Henk van de Hulst presents an opportune moment to take stock of our understanding of the structure, composition, origin and evolution of the interstellar medium of galaxies over cosmic times and chart the future of research in this area. The interstellar medium plays a central role in the evolution of galaxies as the repository of stellar ashes and the birth sites of new stars. Stars in their turn set their environment aglow through their radiation and shape their surroundings with their powerful winds and explosions. This energetic interaction gives rise to multiple ionized, atomic, and molecular phases that interact and interchange material on rapid time scales. A variety of surveys have probed these phases over the years. At the microscopic level, small dust grains and large molecules play an important role in the physics and chemistry of the ISM. These species also provide convenient tracers of the structure of the ISM. Over the last two decades, the Spitzer Space Telescope and the Herschel Space Observatory have opened up the infrared sky to surveys of the ISM. With ALMA on line, JWST on the horizon, and SKA turning into reality, the ISM of galaxies can be probed out to high redshifts. This can be expected to provide much new insight in the evolution of the ISM over the history of the Universe.