SPIRE, the Spectral and Photometric Imaging Receiver, is a submillimetre camera and spectrometer for the European Space Agency's Herschel Space Observatory. It comprises a three-band imaging photometer operating at 250, 360 and 520 μm, and an imaging Fourier Transform Spectrometer (FTS) covering 200-670 μm. The detectors are arrays of feedhorn-coupled NTD spider-web bolometers cooled to 0.3 K. The photometer field of view of is 4 x 8 arcmin., observed simultaneously in the three spectral bands. The FTS has an approximately circular field of view with a diameter of 2.6 arcmin., and employs a dual-beam configuration with broad-band intensity beam dividers to provide high efficiency and separated output and input ports. The spectral resolution can be adjusted between 0.04 and 2 cm-1 (resolving power of 20-1000 at 250 μm). The flight instrument is currently undergoing integration and test. The design of SPIRE is described, and the expected scientific performance is summarised, based on modelling and flight instrument test results.