Polyvalent or multivalent interactions are the simultaneous association of multiple ligands on one entity (a molecule or a surface) to multiple receptors on another entity. Multivalent interactions are ubiquitous in biology - in infectious disease, in processes involving antibodies, in blood clotting, metastasis, platelet activation, inflammation, and in many conditions in which cells interact with surfaces- and have become a focus of study in molecular biochemistry. Multiple simultaneous interactions have unique collective properties that are qualitatively different from the properties of their monovalent constituents. Monovalent interactions- generally small molecules directed towards a single receptor site- are clearly fundamental, but understanding them is not necessarily sufficient to understand multivalency and its importance in biology. Our group is interested in confirming, understanding, and quantifying the importance of multivalency in biological interactions, defining the range of biological systems in which it is important, and moving this fundamental knowledge towards applications in the design of drugs and materials.