The field of topological data analysis is witnessing significant developments, with a growing focus on adapting and extending existing frameworks to handle complex data structures such as weighted directed graphs and time-varying scalar fields. Researchers are exploring new filtration methods, including the walk-length filtration, to analyze the shape and structure of these complex data sets. Additionally, there is a strong emphasis on developing stable and theoretically grounded metrics, such as the Gromov-Wasserstein distance, to compare and analyze topological features of Reeb graphs and other geometric structures. These advances have the potential to significantly improve our understanding of complex data and enable new applications in fields such as network analysis and signal processing. Noteworthy papers include: A Stable and Theoretically Grounded Gromov-Wasserstein Distance for Reeb Graph Comparison using Persistence Images, which proposes a framework for comparing Reeb graphs using a symmetric variant of the Reeb radius and a novel probabilistic weighting scheme. Analyzing Time-Varying Scalar Fields using Piecewise-Linear Morse-Cerf Theory presents an adaptation of Morse-Cerf theory to piecewise-linear functions, enabling the analysis of time-varying scalar fields.