Isogeometric analysis provides a high-order framework for the numerical solution of PDEs. Originally motivated by the integration of numerical simulation with CAD-based geometry, it has shown significant potential as a flexible methodology based on smooth high-degree spline spaces. At the same time, this methodology raises significant theoretical and computational challenges, including structure-preserving discretizations, smooth spline spaces on triangulations and unstructured meshes, immersed methods for complex geometries, local refinement techniques, efficient operator formation, and robust solvers for the resulting linear systems. This minisymposium aims to present and discuss recent advances in these areas. The minisymposium also aims to foster interaction between the isogeometric analysis community and the broader spectral and high-order methods community.