The fracture of materials/structures is a complex and multi-scale process, which is associated with the rupture of atomic bonds. Hence, the evolution of atomistic crack configurations plays a vital role in the macroscopic fracture behavior. With the swift advancement of experimental technology, the cracks at the atomic scale can be detected by high-resolution electron microscopes, and enhanced computing resources have made atomistic simulation a powerful tool to uncover the underlying fracture mechanisms and to investigate the fracture behaviors of various nanostructured materials. In this review article, we first introduced the common loading approaches for atomistic fracture simulations, including uniform loading, velocity gradient loading, K
-field loading and hydrostatic stress loading. After comparing these loading approaches, we further summarized a few methods of calculating fracture toughness based on atomic scale information, including energy release rate method, stress-strain curve integral method, critical stress intensity factor method, cohesive zone method at atomic scale and J
-integral method at atomic scale. Then, we reviewed the latest computational studies on several typical types of nanostructured materials (including single-crystalline, polycrystalline and twin structures, amorphous structures and heterogeneous interface structures), like the crack resistance of passivated single-crystalline silicon solar cells, the brittle-to-ductile transition of amorphous silicon anodes controlled by lithium concentration in lithium-ion batteries, and the spontaneous interface delamination driven by mismatch stress. These study results revealed the underlying mechanisms behind the experimental phenomena, and were in good agreement with the experimental results. The consistence between simulation and experiment results confirms the reliability and accuracy of atomistic fracture simulations. Finally, we highlighted some challenges faced by atomistic simulations for fracture of materials and proposed the potential future directions.