Meshfree methods such as the reproducing kernel particle method (RKPM) are well suited for modeling materials and solids undergoing fracture and damage processes, and nodal integration is a natural choice for modeling this class of problems. However, nodal integration suffers from spatial instability, and the excessive material deformation and damage process could also lead to kernel instability in RKPM. This paper reviews the recent advances in nodal integration for meshfree methods that are stable, accurate, and with optimal convergence. A variationally consistent integration (VCI) is introduced to allow correction of low order quadrature rules to achieve optimal convergence, and several stabilization techniques for nodal integration are employed. The application of the stabilized RKPM with nodal integration for shock modeling, fracture to damage multiscale mechanics, and materials modeling in extreme events, are demonstrated. These include the modeling of man-made disasters such as fragment-impact processes, penetration, shock, and blast events will be presented to demonstrate the effectiveness of the new developments.