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 μm. The photodetector array camera and spectrometer will be capable of imaging photometry and imaging-line-spectroscopy in the 60-210 μm regime with a spectral resolution of ̃175 km s -1, corresponding to a spectral resolving power R̃1500. The spectral and photometric imaging receiver will operate in the 200-650 μm 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 R̃19 to 48 at 520 μm, 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 R̃3×10 6 in the spectral frequency band from ̃480 to 1910 GHz (625-158 μm). This article describes these instruments and the astronomical problems they are expected to address.