Morphogenesis - the generation of biological shape and form - is fascinating, and its study promises to shed light on a wide range of developmental defects and inform strategies for the artificial growth of organs. Recently, the experimental study of morphogenesis has thrived due to a rise in quantitative methods. The resulting avalanche of quantitative data requires us to rethink the scientific method. We need to design quantitative hypotheses through mathematical models, make quantitative experimental predictions, devise methods for quantitative data analysis, and design methods for quantitative inference using models and data. This thesis aims to enable this transition for the integrative analysis of morphogenesis in epithelia, one of the major tissue types in animals. We begin by conducting the first systematic numerical analysis of a widely used cell-based model of epithelia, the vertex model, and estimate to what extent quantitative model predictions may be influenced by parameter values and implementation details. We then apply this model to a key question in developmental biology by constructing a quantitative theory for tissue size control in the embryonic epidermis of the fruit fly Drosophila, using the model to predict the outcomes of future experiments. Subsequently, we devise a method for estimating mechanical parameters of vertex models from imaging data and quantifying the uncertainty associated with such estimates. Finally, we propose a novel algorithm for robust cell tracking in live-imaging microscopy videos of epithelial tissues that illustrates how graph theoretic concepts may be used to overcome challenges in quantitative data analysis. Together, the contributions in this thesis will enable the quantitative study of epithelia for a wide range of applications.