The field of numerical methods for complex physical systems is witnessing significant advancements, driven by the need for more accurate and efficient simulations. Recent developments are focused on improving the stability, accuracy, and robustness of numerical schemes, particularly in the context of multiphysics problems, such as fluid-structure interaction, magnetoelasticity, and elasto-acoustic wave propagation. Notable progress is being made in the development of high-order methods, such as the hybrid high-order (HHO) methods, which offer improved accuracy and flexibility for simulating complex systems. Additionally, advancements in stabilization techniques, like local projection stabilization (LPS) methods, are enabling more robust and reliable simulations. Innovative approaches, such as the maximum likelihood discretization (MLD) and the fast-wave slow-wave spectral deferred correction methods (FWSW-SDC), are being explored to address challenges in simulating complex phenomena, like transport equations and compressible Euler equations. Furthermore, researchers are making significant strides in the development of finite element methods, mechatronic systems, robotics, and control, as well as quasi-Monte Carlo methods and reinforcement learning. Some noteworthy papers in these areas include the introduction of a novel mixed-hybrid finite element method for Kirchhoff-Love shells, the development of parametric reduced order models for mechatronic systems, and the proposal of a new framework for model predictive control. These advancements have the potential to significantly impact the design and optimization of complex systems, enabling the creation of more efficient and reliable components. The use of advanced numerical techniques, such as matrix-free methods and automatic code generation, is also gaining traction, and the development of open-source libraries is facilitating the implementation and comparison of different methods. Overall, the progress being made in these fields is paving the way for more accurate and efficient simulations, and is expected to have a significant impact on a wide range of applications, from speech recognition to robotics and control.