A promising method for growing functional liver tissue in vitro involves culturing hepatocytes as spheroidal cell aggregates. In this thesis, we develop mathematical models of cell aggregation, and use them to determine how hepatocytes' interactions with the extracellular matrix (ECM) on which they are seeded, and with stellate cells, affect the process. Chapters 2-4 focus on the effect that cell-ECM coupling has on the aggregation process. We use a novel formulation that couples a mechanical model for the ECM with a two-phase model for the cell-culture region. A combination of linear stability analysis and numerical simulations are used to identify parameter regimes in which aggregation occurs, and investigate the effect of changing key parameters. In Chapter 2, we assume a one-dimensional geometry, whereas in Chapters 3 and 4, the slender two-dimensional geometry is exploited to obtain two alternative one-dimensional models in which the mechanisms dominating aggregation are chemotaxis and surface tension. In Chapter 5, we focus on interactions between hepatocytes and stellates, neglecting the role of the ECM.We develop new non-local models to investigate the relative contributions of hepatocyte-heaptocyte and hepatocyte-stellate interactions in controlling spheroid formation. Comparison with experimental results suggests that the hepatocyte-stellate interaction is the stronger, in which case a 1:1 seeding ratio of hepatocytes to stellates is likely to be optimal for promoting swift aggregate formation.