The field of numerical methods for hyperbolic conservation laws is moving towards the development of high-order, robust, and efficient schemes that can handle complex problems with high accuracy. Recent research has focused on designing schemes that preserve physical quantities such as positivity, entropy, and equilibrium states, while also capturing shocks and discontinuities accurately. Noteworthy papers in this area include the development of a positivity-preserving well-balanced PAMPA scheme for one-dimensional shallow water models, which can preserve a large family of smooth moving equilibria in a super-convergent manner. Another notable work is the development of a sweeping positivity-preserving high-order finite difference WENO scheme for Euler equations, which can preserve positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. Additionally, research on uncertainty quantification in forward problems has led to the development of CWENO interpolation methods that can mitigate oscillatory behavior and provide accurate estimates of probability density functions and mean values.