Ice wedges are wedge-shaped masses of ice, oriented vertically with their apices downward, a few millimeters to many meters wide at the top, and generally less than 10 m vertically. Ice wedges grow in and are confined to humid permafrost regions. Snow, hoar frost, or freezing water partly fill winter contraction cracks outlining polygons, commonly 5–20 m in diameter, on the surface of the ground. Moisture comes from the atmosphere. Increments of ice, generally 0.1–2.0 mm, are added annually to wedges which squeeze enclosing permafrost aside and to the surface to produce striking surface patterns. Soil wedges are not confined to permafrost. One type, sand wedges, now grows in arid permafrost regions. Sand wedges are similar in dimensions, patterns, and growth rates to ice wedges. Drifting sand enters winter contraction cracks instead of ice. Fossil ice and sand wedges are the most diagnostic and widespread indicators of former permafrost, but identification is difficult. Any single wedge is untrustworthy. Evidence of fossil ice wedges includes: wedge forms with collapse structures from replacement of ice; polygonal patterns with dimensions comparable to active forms having similar coefficients of thermal expansion; fabrics in the host showing pressure effects; secondary deposits and fabric indicative of a permafrost table; and other evidence of former permafrost. Sand wedges lack open-wedge, collapse structures, but have complex, nearly vertical, crisscrossing narrow dikelets and fabric. Similar soil wedges are produced by wetting and drying, freezing and thawing, solution, faulting, and other mechanisms. Many forms are multigenetic. Many socalled ice-wedge casts are misidentified, and hence, permafrost along the late-Wisconsinan border in the United States was less extensive than has been proposed.