SPIRE, the Spectral and Photometric Imaging Receiver, will be an imaging photometer and spectrometer for ESA's Herschel Space Observatory. The main scientific goals and design drivers for SPIRE are deep extragalactic and galactic imaging surveys and spectroscopy of star-forming regions in own and nearby galaxies. It comprises a three-band imaging photometer with bands centred at approximately 250, 360 and 520 μm, and an imaging Fourier Transform Spectrometer (FTS) covering 200-670 μm. The detectors are feedhorn-coupled NTD spider-web bolometers cooled to 300 mK by a recyclable 3He refrigerator with a cycle time of less than two hours and a hold time of more than 46 hours. The photometer field of view is 4 x 8 arcminutes (the largest that can be accommodated) and is observed simultaneously in the three spectral bands. The angular resolution is determined by the telescope diffraction limit, with FWHM beam widths of approximately 17, 24 and 35 arcseconds at 250, 360 and 520 μm, respectively. An internal beam steering mirror allows spatial modulation of the telescope beam, and mapping observations can also be made by drift-scanning the telescope. The FTS has a field of view of 2.6 arcminutes. It uses a dual-beam configuration with novel broad-band intensity beam dividers to provide high efficiency and separated output and input ports. The FTS scanning mirror has a linear travel of up to 3.5 cm, providing adjustable spectral resolution of 0.04-2 cm-1 (λ/Δλ = 20 - 1000 at 250 μm). The instrument design, operating modes, and estimated sensitivity are described.