Understanding the stochastic dynamics and first-passage properties of active and passive particles in complex environments provides the key to identify the physical processes in biological systems. In this project we study various aspects of diffusive or active dynamics of biological agents and develop stochastic models with predictive power. We are particularly interested in optimal search strategies in stochastic (correlated) active search processes, with emphasis on the dynamics of immune cells. We also study the first passage properties of tracer particles and chemical signals in branched structures of neuronal dendrites as well as active transport in narrow sticky channels and along cytoskeletal filaments. Moreover, correlations and memory effects in active processes with distinct motility states, such as the run-and-tumble dynamics of bacteria, will be studied.