Schelling's famous "spatial proximity" model of segregation was first introduced in 1969. His work sets out to explore residential dynamics in populations of ) more than one ethnicity. In particular, the notion of "tolerance" shows how even a small need for familiarity within one's neighbourhood can result in largescale segregation. Schelling's "bounded neighbourhood model", outlined in the same publication, has however received much less attention from economists and mathematicians alike. This thesis provides a mathematical description of the latter model as a nonlinear dynamical system with which to explore the consequences of Schelling's intuition. In particular, we are able to deduce conditions under which segregation is not inevitable. The effect of varying the parameters and inputs of the model is studied in detail, and we use techniques from network theory and nonlinear dynamics in order to develop further variants of the model, beginning with those suggested by Schelling himself. Some new measures are developed that aid in the quantitative description of the equilibria of the model, based on the existing concepts of homophily and modularity. These developments enhance the power of Schelling's model in describing social dynamics. Additional work focuses on the study of networks of social interactions. In particular, we develop the idea of measuring segregation at the level of an individual agent via the use of different measures of centrality. Some simple examples illustrate the need for a range of measures in order to encapsulate an intuitive understanding of this complex phenomenon. This work enriches the toolbox of segregation measures available for future studies, allowing for deeper understanding of the structure of social systems.