The Herschel Space Observatory has revealed a very different galaxyscape from that shown by optical surveys which presents a challenge for galaxy-evolution models. The Herschel surveys reveal (1) that there was rapid galaxy evolution in the very recent past and (2) that galaxies lie on a single Galaxy Sequence (GS) rather than a star-forming 'main sequence' and a separate region of 'passive' or 'red-and-dead' galaxies. The form of the GS is now clearer because far-infrared surveys such as the Herschel ATLAS pick up a population of optically red starforming galaxies that would have been classified as passive using most optical criteria. The space-density of this population is at least as high as the traditional star-forming population. By stacking spectra of H-ATLAS galaxies over the redshift range 0.001 < z < 0.4, we show that the galaxies responsible for the rapid low-redshift evolution have high stellar masses, high star-formation rates but, even several billion years in the past, old stellar populations - they are thus likely to be relatively recent ancestors of early-type galaxies in the Universe today. The form of the GS is inconsistent with rapid quenching models and neither the analytic bathtub model nor the hydrodynamical EAGLE simulation can reproduce the rapid cosmic evolution. We propose a new gentler model of galaxy evolution that can explain the new Herschel results and other key properties of the galaxy population.