The field of numerical methods for partial differential equations (PDEs) and interpolation is experiencing significant developments, driven by the need for more efficient, accurate, and robust algorithms. A key direction is the improvement of existing methods, such as the closest point method, to handle complex boundary conditions and increase their applicability to a broader range of problems. Another area of focus is the development of novel interpolation techniques, like the symmetric wave interpolation method, which aims to balance numerical stability with practical utility. The integration of isogeometric analysis (IgA) with other numerical techniques, such as boundary element methods and multigrid approaches, is also a prominent trend, offering enhancements in accuracy, efficiency, and the ability to tackle complex geometries and high-dimensional problems. Furthermore, advancements in algorithms for specific applications, such as thermal simulation in metal additive manufacturing and the solution of elliptic PDEs with unknown boundary data, demonstrate the field's diverse and innovative nature. Noteworthy papers include the development of a smoothly varying quadrature approach for 3D IgA-BEM discretizations, which enhances accuracy and robustness, and the introduction of a surrogate-informed framework for sparse grid interpolation, which significantly reduces the required number of expensive evaluations. Additionally, advancements in multigrid methods with linear storage complexity and parallel simulation and adaptive mesh refinement for 3D elastostatic contact mechanics problems showcase the field's progress towards more efficient and scalable numerical solutions.