Peridynamics is a nonlocal continuum mechanics approach widely used for modeling damage and fracture phenomena. There are different formulations of the underlying theory to realize the same material behaviors as observed in reality and described by the classical (elastic) theory. A particular problem is that the non-locality induces surface effects near boundaries. The correspondence formulation of peridynamics mitigates these limitations, utilizing an approximated deformation gradient to calculate stress forces. However, although this reformulation improves the accuracy of elastic modeling, it introduces instabilities. These problems combined make it hard to model wave propagation and dynamic fracture with large deformations, especially in thin structures. This contribution presents a comprehensive review of bond-associated peridynamic formulations as a promising solution to these challenges. Various approaches within bond-associated modeling are compared, focusing on computational efficiency and other factors regarding discretization and computational implementation. The analysis confirms that bond-associated models effectively capture the correct fragmentation process in thin structures. Explanatory examples of dynamic fracture in thin structures are provided, showcasing the capabilities and practical relevance of these models.