On April 26-28, 2001, the Board on Mathematical Sciences and Their Applications (BMSA) and the Board on Life Sciences of the National Research Council cosponsored a workshop on the dynamical modeling of complex biomedical systems. The workshop's goal was to identify some open research questions in the mathematical sciences whose solution would contribute to important unsolved problems in three general areas of the biomedical sciences: disease states, cellular processes, and neuroscience. The workshop drew a diverse group of over 80 researchers, who engaged in lively discussions. To convey the workshop's excitement more broadly, and to help more mathematical scientists become familiar with these very fertile interface areas, the BMSA appointed one of its members, George Casella, of the University of Florida, as rapporteur. He developed this summary with the help of two colleagues from his university, Rongling Wu and Sam S. Wu, assisted by Scott Weidman, BMSA director. This summary represents the viewpoint of its authors only and should not be taken as a consensus report of the BMSA or of the National Research Council.