The field of numerical methods for complex media is rapidly advancing, with a focus on developing efficient and accurate methods for solving problems involving high-contrast coefficients, heterogeneous media, and nonlinear partial differential equations. Recent developments have led to the creation of novel multiscale methods, hybridizable discontinuous Galerkin methods, and adaptive nonlinear elimination preconditioning techniques, which have shown significant improvements in computational efficiency and accuracy. These advancements have far-reaching implications for a wide range of applications, including porous media flow, fracture mechanics, and thermo-viscoelasticity. Notable papers in this area include the proposal of a locking-free multiscale method for linear elasticity, which achieves strongly symmetric stress approximations without excessive computational costs. Another significant contribution is the development of a hybridizable discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems, which demonstrates faster convergence rates compared to standard HDG methods. Furthermore, the introduction of online learning techniques to accelerate nonlinear PDE solvers has shown promising results, with reductions in computational time of up to 85%. Overall, these advancements highlight the ongoing efforts to improve the efficiency and accuracy of numerical methods for complex media, with potential applications in various fields of engineering and physics.