The authors present a comprehensive overview of image processing and analysis work done to support research into the model flowering plant Arabidopsis thaliana. Beside the plant's importance in biological research, using image analysis to obtain experimental measurements of it is an interesting vision problem in its own right, involving the segmentation and analysis of sequences of images of objects whose shape varies between individual specimens and also changes over time. While useful measurements can be obtained by segmenting a whole plant from the background, they suggest that the increased range and precision of measurements made available by leaf-level segmentation makes this a problem well worth solving. A variety of approaches have been tried by biologists as well as computer vision researchers. This is an interdisciplinary area and the computer vision community has an important contribution to make. They suggest that there is a need for publicly available datasets with ground truth annotations to enable the evaluation of new approaches and to support the building of training data for modern data-driven computer vision approaches, which are those most likely to result in the kind of fully automated systems that will be of use to biologists.