Structure-preserving numerical methods have emerged as a cornerstone for the reliable simulation of nonlinear PDEs in applied sciences and engineering. For time-evolution problems, it is crucial that numerical schemes reflect fundamental thermodynamic properties such as energy dissipation, entropy production and preservation of conservation laws. These properties underpin the existence and uniqueness of physically meaningful weak solutions and are essential for robust error analysis through relative energy and entropy techniques. This minisymposium will focus on recent advances in the design and analysis of structure-preserving discretization techniques, including finite element, finite volume, and discontinuous Galerkin methods, as well as structure-aware time integration schemes. Emphasis will be placed on methods that guarantee discrete analogues of energy or entropy stability, enabling accurate and robust simulations even for highly nonlinear or multiscale problems. We will highlight both theoretical developments and practical applications, such as energy-stable schemes for phase-field models, entropy-consistent approaches for turbulent flows, and structure-preserving algorithms for coupled multiphysics systems. Special attention will be given to the interplay between discrete stability properties and a priori error estimates, as well as the challenges of implementing these methods in high-performance computing environments. By bringing together experts from numerical analysis, computational physics, and engineering, this minisymposium aims to foster a comprehensive discussion on the state-of-the-art in structure-preserving numerical methods and to identify promising directions for future research and applications.