The Herschel space observatory, a cornerstone mission of the European Space Agency, with a Principal-Investigator-provided science payload, and contributions from the US National Aeronautics and Space Administration, is designed to explore the far-infrared and submillimeter spectral range with a powerful set of astronomical instruments built by multinational consortia of scientists and engineers. Herschel is expected to be launched in the spring of 2007. It will house a 3.5-m. passively cooled telescope and three instruments operating in the wavelength range from 60 to 650 mum. The photodetector array camera and spectrometer will be capable of imaging photometry and imaging-line-spectroscopy in the 60-210 pm regime with a spectral resolution of similar to175 km s(-1), corresponding to a spectral resolving power R similar to 1500. The spectral and photometric imaging receiver will operate in the 200-650 mum range, to map large areas of the sky. It will also carry out low resolution Fourier transform spectroscopy, whose resolution can be varied at least over the range of 1-0.4 cm(-1), corresponding to R similar to 19 to 48 at 520 mum, but with a goal of increasing this range from 2 to 0.04 cm(-1). The heterodyne instrument for the far-infrared will provide very high spectral resolving power up to R similar to 3 x 10(6) in the spectral frequency band from similar to480 to 1910 GHz (625-158 mum). This article describes these instruments and the astronomical problems they are expected to address. (C) 2004 COSPAR. Published by Elsevier Ltd. All rights reserved.