The transport of viscous fluids is a central function of many biomedical systems. We are studying advanced pumping concepts as alternatives to classical pumping systems with, e.g., rotating parts. We focus on pumping concepts with only minimal mechanical impact on the transported fluid and which lend themselves to miniaturization. This includes the concepts of peristaltic action, acoustic or steady streaming phenomena. Our work addresses various applications of such concepts in the clinical context, e.g. therapeutic devices and implants. In most projects we use a combination of computational and experimental methods to obtain a comprehensive picture of a studied biomedical flow system.