The field of numerical analysis is witnessing significant developments in spline-based methods, with a focus on improving accuracy, efficiency, and versatility. Recent research has concentrated on constructing basis functions for polynomial spline spaces over arbitrary partitions, enabling the use of these methods in a wider range of applications. Notably, innovative approaches have been proposed to address dimensional instability and ensure linear independence and completeness of the basis functions. Furthermore, advancements in quadrature rules have led to improved convergence rates and reduced computational costs. These developments have the potential to enhance the accuracy and efficiency of numerical simulations in various fields. Noteworthy papers include: The paper on polynomial preserving recovery for PHT-splines, which proposes a method for obtaining more accurate gradient approximations. The paper on basis construction for polynomial spline spaces over arbitrary T-meshes, which presents a novel method for constructing bases for PT-splines. The paper on the convergence of symmetric triangle quadrature rules, which reveals that quadrature rules capable of integrating polynomials up to even degrees converge faster than expected.