This paper focuses on digitally-supported research methods for an important group of cultural heritage objects, the Greek pottery, especially with figured decoration. The design, development and application of new digital methods for searching, comparing, and visually exploring these vases need an interdisciplinary approach to effectively analyse the various features of the vases, like shape, decoration, and manufacturing techniques, and relationships between the vases. We motivate the need and opportunities by a multimodal representation of the objects, including 3D shape, material, and painting. We then illustrate a range of innovative methods for these representations, including quantified surface and capacity comparison, material analysis, image flattening from 3D objects, retrieval and comparison of shapes and paintings, and multidimensional data visualization. We also discuss challenges and future work in this area.