Virial expansions

The use and the properties of the virial expansion are reviewed and speculations given concerning possible future developments. Firstly an account is given of the methodologies used for calculating the virial coefficients, both in isotropic and liquid crystalline phases. We then consider the isotropic phase, looking at the radius of convergence of the series for one component systems, mixtures and systems with attractive interactions. We next consider the application of a virial analysis to disordered liquid crystalline phases (nematic and cubatic). Finally, we speculate as to future interesting lines of research in this area, in particular the possibility of applying the virial series to positionally ordered phases.