Leukocytes (white blood cells or WBCs) are the first line of host defense against invading pathogens. In inflammation, they are recruited from the blood to sites of infection or injury through a complex series of events, referred to as leukocyte adhesion cascade, which includes initial contact of a leukocyte with activated endothelium (tethering or capture), leukocyte rolling, firm adhesion, and transendothelial migration. While being beneficial for host defense, leukocyte recruitment into inflamed tissues may also lead to various inflammatory disorders, such as asthma, autoimmune diseases, ischemia-reperfusion injury, and atherosclerosis. In this talk, we will discuss the computational model for leukocyte adhesion developed on a basis of our computational fluid dynamics algorithm for fully three-dimensional transient simulations of multiphase viscoelastic flows. In the model, the leukocyte is a viscoelastic cell with the nucleus located in the intracellular space and cylindrical microvilli distributed over the cell membrane. Leukocyte-endothelial cell interactions are mediated by cell adhesion molecules expressed on the tips of leukocyte microvilli and on endothelium. We will show that the model can predict both shape changes and velocities of rolling leukocytes under physiological flow conditions. Results of this study indicate that viscosity of the cytoplasm is a critical parameter of leukocyte adhesion, affecting the cell's ability to roll on endothelium, and that in vitro parallel-plate flow chamber assays underestimate leukocyte adhesion that occurs in the microcirculation. We will also review other biomedical applications of the computational algorithm, including mucus transport in the airways, bubble-vessel wall interaction in shock-wave lithotripsy, and polymer drug delivery systems.