The aim of this thesis is to advance the understanding of auxeticity. This is achieved by developing a more accurate way to classify materials exhibiting the property, by carrying out high-throughput atomistic simulations of framework materials based on the SiO2 and GeO2 chemistries, and by exploring mechanistic models and possible correlations with directional density variations. At first this thesis outlines the development of a typographic system for negative Poisson's ratio. Materials are given classifications based on the degree to which auxetic behaviour is observed along specific axes of deformation and the frequency of occurrence of these axes. A systematic study is then performed on the elastic properties of zeolitic silicon dioxide and germanium dioxide structures. The typology is applied to these materials to better understand their auxetic behaviour. The JST framework is identified as isotropically auxetic, the first crystal to exhibit such general negative Poisson's ratios. An exploration into the effects of local density variations between parallel planes on Poisson's ratio is undertaken, but no clear correlation is found. Finally, software for systematically creating and evaluating two dimensional networks of triangles is produced. The geometrical analysis of these rotating structures predicts a high level of auxeticity and further work into three dimensional equivalents is recommended.