Nonlinear hyperbolic balance laws serve as the mathematical foundation for a vast range of fluid dynamic processes. Despite their widespread use, addressing fundamental hyperbolic phenomena, such as the complex multi-scale interaction of shock waves with shear instabilities, or the coupling of hyperbolic transport with stochastic environments, remains a challenge for numerical modeling. A prominent example is the inadequacy of the classical entropy principle to guarantee unique solutions in continuum-scale systems, often giving rise to highly oscillatory, non-unique flow fields. Consequently, this minisymposium aims to explore recent breakthroughs and novel directions in the design of tailored, robust numerical frameworks for hyperbolic balance laws. We welcome contributions focusing on innovative solution concepts, multi-scale methodologies, and computational approaches for probabilistic fluid dynamics. This scope encompasses high-resolution and high-order discretizations exploiting generalized entropy formulations, dissipative limits, or advanced approaches for non-local and multi-scale problems, such as subgrid-scale modeling within continuum frameworks. Furthermore, emphasis is placed on structure-preserving and stable schemes, including recent advances in entropy-conservative or entropy-stable methods, well-balancing, and the accurate capturing of asymptotic states like low-Mach limits. Finally, the session targets uncertainty quantification and algorithmic developments for stochastic hyperbolic systems, featuring probabilistic formulations for statistical turbulence via stochastic variational principles or hybrid data-driven and filtering techniques. This session serves as a collaborative platform highlighting ongoing research from the German Priority Research Program SPP-2410 (”Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness”), while warmly inviting the broader international community to contribute, exchange ideas, and discuss future trajectories in the numerical analysis and simulation of hyperbolic systems.