The field of numerical methods for partial differential equations (PDEs) is witnessing significant developments, with a focus on improving the accuracy, efficiency, and robustness of existing methods. Researchers are exploring new formulations, such as weighted least-squares minimization and space-time transformations, to enhance the performance of adaptive finite element methods and Galerkin-Bubnov formulations. The use of high-order methods, arbitrary Lagrangian-Eulerian approaches, and moving-mesh finite element algorithms is becoming increasingly popular for solving complex PDE problems, including those with nonlinearities and moving boundaries. Noteworthy papers include: The paper on global convergence of adaptive least-squares finite element methods, which presents a novel approach to linearization and error estimation. The work on higher order unfitted space-time methods, which establishes stability and error bounds for transport problems on moving domains.