The variety of evidence bearing on the nature of space weathering is reviewed. The effects of space weathering include spectral darkening, reddening and subdued absorption bands, and the distinctive magnetic electron spin resonance caused by single-domain metallic iron particles. Ever since the Apollo missions, two paradigms have dominated the thinking of the planetary science community concerning space weathering: (1) the optical effects are caused by impact-vitrified glass in agglutinates, and (2) the submicroscopic metallic iron results from the reduction of ferrous iron by the impact melting of minerals whose surfaces have been saturated with hydrogen from the solar wind. However, studies carried out since the Apollo program showed that both of these paradigms are invalid. A hypothesis first suggested by the author and his colleagues 26 years ago, but not generally accepted at that time, now appears to be essentially correct: Both the optical and magnetic effects are caused by metallic iron particles smaller than the wavelength in ubiquitous vapor-deposited coatings on soil particle surfaces and inside agglutinates. The vapor is generated by both solar wind sputtering and micrometeorite impact vaporization and injected preferentially downward into the porous regolith. The iron is reduced by a physical process, the selective loss of oxygen that occurs during deposition of the vapor, and does not require heating, melting, or a reducing environment. A mathematical theory that describes the optical effects of the submicroscopic iron quantitatively is derived and applied to the regoliths of the Moon, Mercury and an S asteroid. ¿ 2001 American Geophysical Union