The main theme of my research is to understand the interplay between the microscopic motion of particles and the transport properties of systems composed of many such particles on a macroscopic scale. The microscopic dynamics, given by the equations of motion of single particles, is often highly nonlinear in terms of chaos and very complicated by featuring spatio-temporal correlations. This often leads to non-trivial, unexpected transport properties of diffusion or (electrical, heat) conduction in statistical many-particle systems under nonequilibrium conditions induced by external gradients or fields. In previous work I discovered a fractal parameter dependence of transport coefficients in chaotic dynamical systems and analysed relations between microscopic chaos and macroscopic transport in dissipative dynamical systems. More recently I got interested in anomalous transport phenomena emerging from microscopic dynamics that is much stronger correlated than ordinary Brownian motion. This theory is applied to understand experiments on biological cell migration and on the foraging of bumblebees. I also started to work on computer simulations of single-molecule diffusion in nanopores. My research in theoretical physics and applied mathematics thus stretches over the whole range from mathematical foundations towards experimental applications.