Over the past four decades, Chi-Wang Shu has profoundly shaped the field of computational mathematics through pioneering contributions to high-order numerical methods, hyperbolic conservation laws, discontinuous Galerkin methods, strong stability preserving time discretizations, and scientific computing. In celebration of his 70th birthday, this minisymposium brings together distinguished researchers whose work reflects the breadth and continuing impact of his scientific legacy. The presentations highlight recent advances in numerical methods for partial differential equations, including wave propagation, multiscale computation, adaptive algorithms for hyperbolic conservation laws, high-order time integration, and the mathematical analysis of numerical stability and accuracy. Together, these talks showcase both the enduring influence of Professor Shu’s ideas and the exciting new directions they continue to inspire across computational mathematics.