Morphogenesis emerges from complex interactions between genetic, cell-cell signaling and mechanical processes. To understand these processes, it is essential to be able to quantify cell shape change and gene expression at cellular resolution over multiple time points. Ideally, a full 3D quantification of cell shape and gene expression, with changes over time, is desired. However this is often technically challenging in opaque plant tissue. Equally challenging is the modeling of growth and cell division in full 3D. Fortunately, many biological processes occur on surface layers of cells, and 2D models can be used. However on highly curved surfaces, flat projections can introduce too much distortion to accurately record the dynamics of growth experimentally. To address this problem we have developed MorphoGraphX, a software that enables image processing on curved surface meshes. Many image processing algorithms designed for 2D and 3D images can be adapted to work with these “2.5D” images, such as cell segmentation and lineage tracking. Several examples of the use of the software on different plant organs will be presented, followed by our inroads towards developing an integrated environment for computational morphodynamics on surfaces.