Nonlocal models offer a robust framework for understanding and addressing complex real-world challenges where classical theories prove inadequate, particularly in the study of materials and structures characterized by discontinuities, singularities, and long-range interactions. Peridynamics, a reformulation of continuum mechanics based on integral equations, offers a mathematically sound framework that avoids spatial derivatives and naturally enables the modeling of crack initiation, propagation, and other discontinuous phenomena. Capturing the dynamics of such systems poses significant computational and analytical challenges due to their nonlocality and inherently multiscale nature. In addition to exhibiting discontinuous solutions, these problems are characterized by non-sparse stiffness matrices and singular convolution kernels. These intrinsic features lead to a significant increase in computational complexity and motivate the development of efficient and innovative solution strategies. This mini-symposium aims to address recent advances in both the theoretical and computational aspects of nonlocal methods, with a focus on applications to multiscale problems involving fracture and material discontinuities. The mini-symposium will bring together contributions spanning a broad range of methodologies and approaches, including, but not limited to, material failure, variational methods, robust numerical methods for complex structural analysis, finite and virtual element methods for crack simulation, multiscale modeling techniques, hybrid data-driven and physics-based approaches, reduced-order modeling and innovative techniques for uncertainty quantification and optimal control.