The field of numerical methods for hyperbolic systems is moving towards the development of more accurate and robust schemes for solving complex problems. Researchers are focusing on creating well-balanced methods that can handle non-conservative hyperbolic partial differential equations with source terms, as well as developing frameworks for embedding general conservation constraints in discretizations of hyperbolic systems on arbitrary meshes. Additionally, there is a growing interest in structure-preserving numerical calculations and asymptotically compatible entropy-consistent discretizations for nonlocal conservation laws. Noteworthy papers in this area include: A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms, which provides new insights into the impact of discretizations on numerical solutions. Asymptotic preserving schemes for hyperbolic systems with relaxation, which presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms.