Examples for hydrodynamic collective modes are sound waves, shear and diffusive modes. But what are non-hydrodynamic collective modes? Most physicists likely have never ever heard about non-hydrodynamic modes in their entire career. Indeed, there does not seem to be a single textbook on this topic. This colloquium will give an introduction to the physics of non-hydrodynamic modes, featuring gravitational waves, string theory predictions for experiment, the coolest and hottest stuff on earth and high-temperature superconductors.