Interfacial physics is a rich area of study with many practical manife
stations and significant complexity inherent in the underlying two-dim
ensional behaviour. For example, structures formed from aggregates of
self-assembled amphiphiles may show a variety of forms and properties
ranging from ordered arrays of micelles to disordered, bicontinuous mi
croemulsions. Any theoretical study of this behaviour must begin with
a characterization of both the shape and energetic state of the interf
ace. Often one has terms in the energy that depend on both the area (e
.g. surface tension) and the curvature. We present a review of the var
ious ''curvature measures'' that have historically been employed to ev
aluate the degree of surface bending, and their relationship to both t
he generalized theory of capillarity and the form of the corresponding
equilibrium conditions (e.g. the Young-Laplace equation of capillarit
y).