An increasing human population faces the growing demand for agricultural products and accurate global climate models that account for individual plant morphologies to sustain human life. Both demands are ultimately rooted in an improved understanding of the mechanistic origins of plant development and their resulting phenotypes. Such understanding requires geometric and topological descriptors to characterize plant phenotypes and to link phenotypes to genotypes. However, the current plant phenotyping framework relies on simple length and diameter measurements, which fail to capture the exquisite architecture of plants. My research aims to set new frontiers in combining plant phenotyping with recent results from shape theory at the interface of geometry and topology. The core technical method I use is to expand and apply the mathematical concept of a “shape descriptor” to the plant sciences. Shape descriptors describe the current state and growth of complex structures, including the rich geometric and topological characteristics of plants. More generally, understanding adaptation of plants to their environments is best observed within imaging data capturing the spatial arrangement of plant organs forming the plant phenotype. Spatial arrangements appear in leafs, branches, roots etc. on all biological scales. A full understanding the formation of morphological phenotypes requires analysis of the interplay with the underlying formation processes on cellular and genetic scales. Applying and extending shape theory for plants is the centerpiece of my current work towards unravelling the formation of plant phenotypes. In doing so, I utilize data collected with various imaging instruments from which shapes are extracted to apply shape descriptions.