The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative techniques for solving high-dimensional problems, improving scalability, and enhancing accuracy. Recent developments have centered around the creation of new methods, such as the neural semi-Lagrangian approach, which combines the benefits of semi-Lagrangian methods with the power of neural networks to tackle high-dimensional advection-diffusion problems. Additionally, researchers have been exploring the use of adaptive methods, like the p-adaptive polytopal discontinuous Galerkin method, to efficiently approximate brain electrophysiology models. Furthermore, there has been significant progress in the development of model order reduction techniques, including the space-time Galerkin reduced basis method, which has been successfully applied to simulate hemodynamics in arteries. Noteworthy papers include the introduction of a hybrid framework for efficient Koopman operator learning, which enables the discovery of linear operators and explicit mappings for complex systems, and the proposal of a novel substructuring approach for mitigating the potential ill-posedness of local Dirichlet problems for the Helmholtz equation. The neural semi-Lagrangian method has shown great promise in high-dimensional numerical experiments. The proposed substructuring approach has demonstrated robust convergence rates and scalability, even for large wavenumbers.