We have carried out two extremely deep surveys with SPIRE, one of the two cameras on Herschel, at 250 μm, close to the peak of the far-infrared background. We have used the results to investigate the evolution of the rest-frame 250-μm luminosity function out to z = 2. We find evidence for strong evolution out to z ≃ 1 but evidence for at most weak evolution beyond this redshift. Our results suggest that a significant part of the stars and metals in the universe today were formed at z preceq 1.4 in spiral galaxies. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. ; DOI: 10.1051/0004-6361/201014675; eprintid: arXiv:1005.2189