The field of numerical methods for solving partial differential equations (PDEs) is moving towards developing more robust and efficient methods for handling complex geometries and nonlinear equations. Recent developments have focused on creating methods that can accurately and efficiently solve problems in domains with curved boundaries, corners, and higher-order interaction terms. One of the key directions is the development of level-set based methods, which have been shown to be effective in handling complex geometries. Another area of research is the development of iterative methods for solving nonlinear equations, such as the elliptic Monge-Ampere equation. Geometrically robust unfitted boundary methods are also being developed, which can handle complex geometries without the need for mesh generation. Additionally, novel approaches such as the Closest Point Heat Method are being introduced for solving Eikonal equations on implicit surfaces. Noteworthy papers include: The paper on the level-set based finite difference method, which presents a novel approach for calculating the ground states of Bose Einstein condensates in domains with curved boundaries. The paper on the Closest Point Heat Method, which introduces a novel approach for solving the surface Eikonal equation on general smooth surfaces.