It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play a central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses cause dramatic departures from classic theories for wetting (Young–Dupré), adhesion (Johnson–Kendall–Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

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