This minisymposium focuses on recent advances in efficient and high-order numerical methods for atmospheric applications, e.g., in dynamical cores used for numerical weather prediction or climate modeling. Typically, the governing equations are the compressible Euler equations on the sphere or related models. Topics of interest include efficient time integration methods (e.g., horizontally-explicit and vertically-implicit (HEVI) methods), structure-preserving discretizations (e.g., energy-conserving, entropy-stable, well-balanced, asymptotic-preserving methods), robustness (e.g., bounds/positivity-preserving methods and schemes able to handle under-resolved flows), subgrid scale modeling for these methods, adaptivity (of models or in space/time), and the design of efficient and scalable (open-source) software. This minisymposium is intended to bring together researchers with different backgrounds, e.g., numerical analysis of compressible flows, high-performance scientific computing, and atmospheric sciences to foster discussions and collaborations.