The zodiacal light is the dominant source of the mid-infrared sky brightness seen from Earth, and exozodiacal light is the dominant emission from planetary and debris systems around other stars. We observed the zodiacal light spectrum with the mid-infrared camera ISOCAM over the wavelength range 5-16 mum and a wide range of orientations relative to the Sun (solar elongations 68degrees-113degrees) and the ecliptic (plane to pole). The temperature in the ecliptic ranged from 269 K at solar elongation 68degrees to 244 K at 113degrees, and the polar temperature, characteristic of dust 1 AU from the Sun, is 274 K. The observed temperature is exactly as expected for large (> 10 mum radius), low-albedo (< 0.08), rapidly-rotating, gray particles 1 AU from the Sun. Smaller particles (< 10 mum radius) radiate inefficiently in the infrared and are warmer than observed. We present theoretical models for a wide range of particle size distributions and compositions; it is evident that the zodiacal light is produced by particles in the 10-100 mum radius range. In addition to the continuum, we detect a weak excess in the 9-11 mum range, with an amplitude of 6% of the continuum. The shape of the feature can be matched by a mixture of silicates: amorphous forsterite/olivine provides most of the continuum and some of the 9-11 mum silicate feature, dirty crystalline olivine provides the red wing of the silicate feature (and a bump at 11.35 mum), and a hydrous silicate (montmorillonite) provides the blue wing of the silicate feature. The presence of hydrous silicate suggests the parent bodies of those particles were formed in the inner solar nebula. Large particles dominate the size distribution, but at least some small particles (radii similar to1 mum) are required to produce the silicate emission feature. The strength of the feature may vary spatially, with the strongest features being at the lowest solar elongations as well as at high ecliptic latitudes; if confirmed, this would imply that the dust properties change such that dust further from the Sun has a weaker silicate feature. To compare the properties of zodiacal dust to dust around other main sequence stars, we reanalyzed the exozodiacal light spectrum for beta Pic to derive the shape of its silicate feature. The zodiacal and exozodiacal spectra are very different. The exozodiacal spectra are dominated by cold dust, with emission peaking in the far-infrared, while the zodiacal spectrum peaks around 20 mum. We removed the debris disk continuum from the spectra by fitting a blackbody with a different temperature for each aperture (ranging from 3.7" to 27"); the resulting silicate spectra for beta Pic are identical for all apertures, indicating that the silicate feature arises close to the star. The shape of the silicate feature from beta Pic is nearly identical to that derived from the ISO spectrum of 51 Oph; both exozodiacal features are very different from that of the zodiacal light. The exozodiacal features are roughly triangular, peaking at 10.3 mum, while the zodiacal feature is more boxy, indicating a different mineralogy. (C) 2003 Elsevier Inc. All rights reserved.