We employ data-driven mathematical modeling of biological function, in order to understand principles of information processing in cells and tissues, as well as self-organization of functional biological structures. As a specific example for information processing performed by biological cells, we characterize a distinct navigation strategy for gradient-sensing along helical paths, which is employed e.g. by marine sperm cells. Cellular swimmers together with their motility control mechanisms allow us to address the adaptation of cellular dynamics to sensing noise and intrinsic fluctuations in an exemplary case. Quantitative comparison with experimental data confirmed the mathematical models. As a second theme, we address self-organization of functional structures in cells and tissues. Specifically, we address the self-assembly of periodic cytoskeletal patterns, as found in the force-generating myofibrils in muscle cells, as well as design principles of liver tissue. In all our research, we combine analytically tractable minimal mathematical models of nonlinear biological dynamics with stochastic simulations. This combination allows for both mechanistic insight and for quantitative comparison with experiments.