Peterson's interests are in species and generic relationships, and biogeographical patterns in the grasses (Poaceae). His specialty is biosystematic studies of the grasses using a multitude of techniques ranging from in depth morphological, anatomical, cytological, micromorphological, molecular, cladistic, and population based genetic studies using soluble enzymes. He has completed revisionary studies in large grass genera, such as: Eragrostis, Muhlenbergia, and Sporobolus, all important forage grasses. He is currently serving as editor of our department's periodical, Contributions from the United States National Herbarium