Block copolymer single crystals (BCPSCs) have attracted widespread attentions due to their unique two-dimensional (2D) structure, good controllability, and great potential applications in recent years. In this paper, the morphology, surface structure of BCPSCs and the related influencing factors are reviewed. We also summarize the studies of 2D crystalline assemblies of block copolymers (BCPs) driven by crystallization and intermolecular π-π interaction. Moreover, the functionalization and properties of BCPSCs and 2D crystalline assemblies of BCPs are introduced. Finally, we put forward some unsolved problems in this field.