Chemotaxis is the directed movement of bacteria, eukaryotic cells, or multi-cellular organisms toward concentrations of environmental chemoattractants. Chemotaxis models have been used extensively to model processes such as migratory behavior, pattern formation, and aggregation phenomena. Haptotaxis is the directed movement of cells controlled by the relative strengths of peripheral adhesions forming arrangement into complex and ordered tissues. Cell movement in morphogenesis, in?ammation, wound healing, tumor invasion and other migrations are the result of haptotactic responses of cells to differential adhesion strengths. Partial differential equations models of chemotaxis and haptotaxis will be presented.