The field of graph theory is moving towards a deeper understanding of the relationship between graph structure and logical expressibility. Recent research has focused on the expressive power of first-order logic with counting quantifiers, and the development of new methods for analyzing graph properties. A key direction is the study of graph classes with bounded treedepth and treewidth, and the use of combinatorial techniques to replace traditional logical methods. Notably, innovative approaches are being explored to characterize graph classes and develop efficient algorithms for computing graph properties. Some papers are particularly noteworthy, including one that provides a generalized version of Courcelle's theorem using connection matrices, and another that presents a practical algorithm for computing 2-admissibility. These advances are expected to have significant implications for the field, enabling more efficient analysis and computation of graph properties.