The study of morphogenesis - the generation of biological shape and form - 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 data motivates us 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. In this talk, I describe our recent work on the integrative analysis of morphogenesis in epithelia, one of the major tissue types in animals. Focusing on a widely used cell-based model of epithelia, the vertex model, I discuss to what extent quantitative model predictions may be influenced by parameter values and implementation details. Next, I illustrate how such models can be used to help gain mechanistic insights into, and generate quantitative predictions on, morphogenetic processes such as tissue size control and axis extension. I then outline a method for estimating mechanical parameters of vertex models from imaging data and quantifying the uncertainty associated with such estimates. Together, these contributions help enable the quantitative study of epithelia for a wide range of applications.