  Recent experiments have shown that surface stresses in soft materials can
have a significant strain-dependence. Here we explore the implications of this
surface elasticity to show how, and when, we expect it to arise. We develop the
appropriate boundary condition, showing that it simplifies significantly in
certain cases. We show that surface elasticity's main role is to effectively
stiffen a solid surface's response to in-plane tractions, in particular at
length-scales smaller than a characteristic elastocapillary length. We also
investigate how surface elasticity effects the Green's-function problem of a
line force on a flat, linear-elastic substrate. There are significant changes
to this solution, especially in that the well-known displacement singularity is
regularised. This raises interesting implications for soft phenomena like
wetting contact lines, adhesion and friction. Finally, we discuss open
questions, future directions, and close ties with existing fields of research.
