The Spectral and Photometric Imaging REceiver (SPIRE), is the Herschel Space Observatory`s submillimetre camera and spectrometer. It contains a three-band imaging photometer operating at 250, 350 and 500 mu m, and an imaging Fourier-transform spectrometer (FTS) which covers simultaneously its whole operating range of 194-671 mu m (447-1550 GHz). The SPIRE detectors are arrays of feedhorn-coupled bolometers cooled to 0.3 K. The photometer has a field of view of 4' x 8', observed simultaneously in the three spectral bands. Its main operating mode is scan-mapping, whereby the field of view is scanned across the sky to achieve full spatial sampling and to cover large areas if desired. The spectrometer has an approximately circular field of view with a diameter of 2.6'. The spectral resolution can be adjusted between 1.2 and 25 GHz by changing the stroke length of the FTS scan mirror. Its main operating mode involves a fixed telescope pointing with multiple scans of the FTS mirror to acquire spectral data. For extended source measurements, multiple position offsets are implemented by means of an internal beam steering mirror to achieve the desired spatial sampling and by rastering of the telescope pointing to map areas larger than the field of view. The SPIRE instrument consists of a cold focal plane unit located inside the Herschel cryostat and warm electronics units, located on the spacecraft Service Module, for instrument control and data handling. Science data are transmitted to Earth with no on-board data compression, and processed by automatic pipelines to produce calibrated science products. The in-flight performance of the instrument matches or exceeds predictions based on pre-launch testing and modelling: the photometer sensitivity is comparable to or slightly better than estimated pre-launch, and the spectrometer sensitivity is also better by a factor of 1.5-2.