In this talk, we shall discuss the opportunities and challenges presented by biological models which rely on numerical simulation and mathematical methods. Mathematical biology is an interdisciplinary fast growing science and needs to benefit from the computer science as well. Based on the existing software packages for the numerical simulation of complex fluid flows (FeatFlow), new numerical methods and algorithmic tools have been developed to deal with the challenging models in bioengineering applications, as for instance, fluid-stucture interaction with elastic vessels, particulate flow, or viscoelastic fluid models. To illustrate some of these numerical techniques we restrict our talk to nonlinear fluids, as for instance, blood flow in the cardiovascular system, which are modeled by non-Newtonian models in complex geometry.