In this dissertation we consider the effect of mechanical interactions on cell biology and how this translates into tissue-level properties in metazoan epithelia. We delineate three model-based approaches with different phenomenological aims and compare applicable results to experimental data. We first consider cellular vertex model simulations, which are used to represent the mechanics of two-dimensional epithelial cell arrays. We outline the assumptions, parameters, and outputs. Then we review a number of systems in which these simulations have been used. The second approach is the Mechanical Inverse, which is a vertex model-based approach to inferring mechanical stresses from cell boundary labeled images of epithelial tissue. We develop this inference method from the assumption of mechanical equilibrium and dominant stresses in the tissue. We then apply this computational method to experimental images and validate the performance. In the final part we consider avian cochlea development in epithelia where lateral inhibition plays a role in cell differentiation---a process which involves cell division, differentiation, and rearrangement in a two-dimensional epithelial layer. We develop a mean-field mathematical description of this process. The results provide a description of the observed hair cell patterns in the cochlea.