Stars form in embedded star clusters which play a key role in determining the properties of a galaxy's stellar population. A large fraction of newly born massive stars are shot out from dynamically unstable embedded-cluster cores spreading them to large distances before they explode. Embedded clusters blow out their gas once the feedback energy from the new stellar population overcomes its binding energy, leading to cluster expansion and in many cases dissolution into the galaxy. Galactic disks may be thickened by such processes, and some thick disks may be the result of an early epoch of vigorous star-formation. Binary stellar systems are disrupted in clusters leading to a lower fraction of binaries in the field, while long-lived clusters harden degenerate-stellar binaries such that the SNIa rate may increase by orders of magnitude in those galaxies that were able to form long-lived clusters. The stellar initial mass function of the whole galaxy must be computed by adding the IMFs in the individual clusters. The resulting integrated galactic initial mass function (IGIMF) is top-light for SFRs < 10 M⊙/yr, and its slope and, more importantly, its upper stellar mass limit depend on the star-formation rate (SFR), explaining naturally the mass–metallicity relation of galaxies. Based on the IGIMF theory, the re-calibrated Hα-luminosity–SFR relation implies dwarf irregular galaxies to have the same gas-depletion time-scale as major disk galaxies, implying a major change of our concept of dwarf-galaxy evolution. A galaxy transforms about 0.3 per cent of its neutral gas mass every 10 Myr into stars. The IGIMF-theory also naturally leads to the observed radial Hα cutoff in disk galaxies without a radial star-formation cutoff. It emerges that the thorough understanding of the physics and distribution of star clusters may be leading to a major paradigm shift in our understanding of galaxy evolution.