Plants, algae, and fungi are essential for nearly all life on earth. Through
photosynthesis, plants and algae convert solar energy to chemical energy in the form of
organic compounds that sustains essentially all life on earth. In addition, plants and
algae convert the carbon dioxide produced by respiring organisms to oxygen that is needed
for respiration. Fungi decompose complex organic compounds produced by respiring organisms
so that molecules can be recycled in photosynthesis and respiration. Plants, algae, and
fungi have one important feature in common, their cells have walls. Expansive growth and
its 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 information
relevant to expansive growth of cells with walls. Mathematical models have been
constructed in an attempt to organize and evaluate this information, to gain insight, to
evaluate hypotheses, and to assist in the selection and development of new experimental
studies. In this article some of the mathematical models constructed to study expansive
growth of cells with walls are reviewed. It is nearly impossible to review all relevant
research conducted in this area. Instead, the review focuses on the development of
mathematical equations that have been used to model expansive growth, morphogenesis, and
growth rate regulation of cells with walls. Also, relevant experimental findings are
reviewed, conceptual models are presented, and suggestions for future research are
proposed. The authors have attempted to provide an overview that is accessible to
researchers that are not working in this field.