Plants, algae, and fungi are essential for nearly all life on earth. Throughphotosynthesis, plants and algae convert solar energy to chemical energy in the form oforganic compounds that sustains essentially all life on earth. In addition, plants andalgae convert the carbon dioxide produced by respiring organisms to oxygen that is neededfor respiration. Fungi decompose complex organic compounds produced by respiring organismsso that molecules can be recycled in photosynthesis and respiration. Plants, algae, andfungi have one important feature in common, their cells have walls. Expansive growth andits regulation are central to the life and development of plant, algal, and fungal cells,i.e. cells with walls. In recent decades there has been an explosion of informationrelevant to expansive growth of cells with walls. Mathematical models have beenconstructed in an attempt to organize and evaluate this information, to gain insight, toevaluate hypotheses, and to assist in the selection and development of new experimentalstudies. In this article some of the mathematical models constructed to study expansivegrowth of cells with walls are reviewed. It is nearly impossible to review all relevantresearch conducted in this area. Instead, the review focuses on the development ofmathematical equations that have been used to model expansive growth, morphogenesis, andgrowth rate regulation of cells with walls. Also, relevant experimental findings arereviewed, conceptual models are presented, and suggestions for future research areproposed. The authors have attempted to provide an overview that is accessible toresearchers that are not working in this field.