The field of numerical methods for differential equations and conservation laws is moving towards the development of more efficient, accurate, and robust schemes. Researchers are focusing on creating methods that preserve the underlying physical properties of the systems being modeled, such as energy conservation, entropy inequality, and invariant regions. There is also a growing interest in developing schemes that can handle complex problems, including non-local conservation laws and mean field games with non-differentiable Hamiltonians. Noteworthy papers in this regard include the introduction of a novel spectral analysis tool for generalized locally Toeplitz sequences, a structure-preserving scheme for the Godunov-Peshkov-Romenski model of continuum mechanics, and an Active Flux method for the Euler equations based on the exact acoustic evolution operator. Additionally, new high-order finite volume schemes are being developed for multispecies kinematic flow models, and numerical methods are being proposed for Lagrangian particle classification and Lagrangian flux calculation.