The KATRIN experiment will determine the neutrino mass with unprecedented accuracy by measuring the endpoint region of the energy spectrum from tritium beta-decay with a high resolution electrostatic spectrometer. Here we describe the demanding requirements and solutions for our vacuum and cryogenic systems. The vacuum system has to reduce the flow of tritium molecules between the windowless gaseous tritium source and the electrostatic spectrometer by 14 orders of magnitude. The vacuum components used to pump out tritium have to be radiation hard. The huge main spectrometer vessel with a volume of 1240 m3 and its complex wire electrode system have to be maintained at a vacuum of 10-11 mbar in order to keep the background rate below 10 mHz. The major tasks of the cryogenic system are the cooling of the super-conducting magnets, stabilization of the temperature of tritium gas in the source below the 10-3 level, cryosorption of tritium on argon frost in the cryogenic pumping section and capturing radon atoms in the main spectrometer with nitrogen cooled cryo-baffles.