This minisymposium is devoted to recent developments in numerical methods for the approximation of hyperbolic partial differential equations (PDEs). A key difficulty in the study of such problems lies in the formation of discontinuities and the presence of multiple scales, requiring the use of advanced numerical schemes [1,2]. Hyperbolic PDEs and their numerical treatment remain an active area of research in applied mathematics due to their theoretical challenges and wide range of applications. Particular relevance is found in fluid dynamics, where hyperbolic models arise in compressible flows, shallow water equations, and multiphase systems, among others. This session brings together contributions addressing these issues from different methodological perspectives. The session highlights recent progress in the construction and mathematical analysis of numerical schemes specifically designed for hyperbolic systems. Special emphasis is placed on high-order methods, structure-preserving techniques, and relaxation-based formulations, among others. In addition to the development of numerical schemes, the session is open to contributions on theoretical aspects such as consistency, stability, and convergence, as well as numerical tests that assess their performance. Both real-world applications of hyperbolic systems—especially in fluid dynamics—and more theoretical research are welcome. REFERENCES [1] E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd Edition, Springer, 2009. [2] R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd Edition, Birkhäuser, 1992.