A geometric approach to microemulsions and other phases in surfactant systems is presented. The basic premise is that the behaviour of these systems is dominated by geometric constraints on microstructure. The utility of this approach is first demonstrated for the one-dimensional fluid, for which the statistical mechanics can be solved analytically, before being applied to more realistic but complex systems. Small-angle X-ray and neutron scattering techniques are used to obtain structural information. A numerical method for calculating theoretical scattering curves from arbitrary models is presented. The importance of the real-space correlation function is emphasised, and it is used to obtain a plot of the scale dependence of the internal surface. A new technique is proposed for the division of two spectra from the same sample measured at different contrasts, which eliminates the underlying lattice and gives sensitive local information. Two new geometric models for microemulsions are presented: a structure of interconnected cylinders and one of folded connected lamellae. It is shown that these models succeed where all others fail, in explaining the behaviour of the isotropic liquid phases found in ternary systems containing the double-chained cationic surfactant didodecyldimethylammonium bromide. This approach is also applied to two nonionic polyoxyethylene surfactant binary systems. Similar methods are also applied to cubic liquid crystalline phases. It is shown by a simple calculation that the scattering from such structures is very sensitive to small changes. Certain of these structures are thought to follow periodic minimal surfaces. Approximations to these are investigated and in particular it is shown that periodic equipotential surfaces and periodic minimal surfaces with the same symmetry and topology are not necessarily identical.