Many systems of partial differential equations arising in physics and engineering are endowed with intrinsic geometric, analytic, and thermodynamic structures. These include involution constraints, such as the divergence-free condition of magnetic fields or the curl-free character of deformation tensor, thermodynamic compatibility requirements encoded in energy conservation and entropy balance or inequalities, and physical admissibility constraints such as positivity of density and pressure. At the same time, these PDE systems are often genuinely multiscale. Important examples include low-Mach-number flows, stiff relaxation systems, and hyperbolic reformulations of parabolic models, where the correct limiting behavior must be recovered in asymptotic regimes. These features make the design of reliable numerical methods particularly demanding: schemes should be accurate and robust, while preserving, at the discrete level, the fundamental structural properties of the continuous problem. The aim of this minisymposium is to review recent advances in high order structure-preserving methods for multiscale PDE systems, with emphasis on the preservation of involutions, thermodynamic compatibility, asymptotic limits, and physical admissibility constraints. Contributions will cover both methodological developments and applications, including continuum mechanics, plasma flows, electromagnetics, and multi-material flows.