Galaxies are born in the very early Universe. Depending on their properties (mainly on their mass and environment), most of them are still forming today. Galaxies are systems that transform gas into stars, and they are still doing so despite the fact that the galaxies exhaust their gas reservoir in a very short time-scale. The question arises as to where the gas that keep them alive comes from. The answer is clear from the point of view of the numerical simulations of galaxy formation: metal-poor gas is continuously accreted from the cosmic web filaments (e.g., Dekel+09). However, the hypothetical cosmological gas inflow has been extremely difficult to detect observationally (e.g., SA+14). The talk will describe the theoretical framework that explains the formation of galaxies in a cosmological context, the key role played by the accretion of cosmic web gas, and the evidence that we have of the process at work. (Some of this evidence has been gathered by our group; e.g., SA+15.) In a sense, the situation is similar the 'quiet revolution' that happened in Solar Physics around the year 2000, when the quiet sun magnetic fields were theoretically predicted (Cattaneo 99) but when observations only hinted at their existence (e.g., SA+ 11).