  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 an 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 causes dramatic departures
from classic theories for wetting (Young-Dupr\'{e}), 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.
