Colloquium

New techniques in cell and molecular biology have produced a better understanding of cell-level processes that has in turn led to better cell-level models for problems ranging from biofilm formation to embryonic development and cancer. However this raises the problem of how to incorporate detailed descriptions of individual-level behavior, be it at the cell, tissue or organ level, into population level descriptions. We will illustrate the mathematical and computational challenges involved with a number of examples ranging from pattern formation in bacteria to hybrid models for tumor growth, and will discuss some of the open problems in this area.