The field of numerical methods for hyperbolic conservation laws is experiencing significant growth, with a focus on developing innovative techniques for solving complex problems. Recent research has centered around improving the accuracy and stability of numerical methods, particularly in the context of high-order methods and well-balanced schemes. One notable area of development is the use of active flux methods, which have shown promise in capturing discontinuities and preserving physical properties. Additionally, there is a growing interest in applying collocation methods and Lax-Wendroff flux reconstruction to solve balance laws and relativistic hydrodynamics equations. Noteworthy papers include:

• A New Semi-Discrete Finite-Volume Active Flux Method for Hyperbolic Conservation Laws, which introduces a novel active flux method with overlapping finite-volume meshes.
• Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws, which presents a new technique for solving local non-linear problems using collocation RK methods.