MathEnergy - Mathematical key technologies for evolving energy grids. In For a sustainable and CO2 neutral power supply, the entire energy cycles for power, gas and heating grids have to be taken into account simultaneously. Despite rapid progress, the energy industry is insufficiently equipped for the superordinate planning, monitoring and control tasks, based on increasingly large and coupled network simulation models. The German MathEnergy project aims to overcome these shortcomings by developing selected mathematical key technologies for energy networks and respective software. This chapter gives an overview of MathEnergy by discussing selected new developments related to model order reduction for gas networks, state estimation for gas and power networks, as well as cross-sectoral modeling, simulation and ensemble analysis. Several new theoretical results as well as related software prototypes are introduced. Results for selected gas and power networks are presented, including a first version of the partDE-Hy demonstrator for analysis of power-to-gas scenarios.