This project is devoted to low-energy nucleon structure and provides the theory component for several experimental programs of this CRC, most notably, the laser spectroscopy of muonic atoms at PSI, and the electron and Compton scattering experiments at MAMI and MESA. A prime goal is to refine the current theoretical predictions for the Lamb shift and hyperfine splitting in muonic hydrogen, deuterium and ³He, with the main focus on nuclear- and nucleon-structure contributions, in particular on two-photon exchange (2PE). The methods of choice are Effective Field Theories and data-driven dispersive evaluations, which require nucleon electromagnetic form factors and polarizabilities as input.