ABSTRACTThe two-dimensional (2D) material family can be regarded as the extreme externalization form of the matter in the planar 2D space. These atomically thin materials have abundant curvature structures, which will significantly affect their atomic configurations and physicochemical properties. Curvature engineering offers a new tuning freedom beyond the thoroughly studied layer number, grain boundaries, stacking order, etc. The precise control of the curvature geometry in 2D materials can redefine this material family. Special attention will be given to this emerging field and highlight possible future directions. With the step-by-step achievement in understanding the curvature engineering effect in 2D materials and establishing reliable delicate curvature controlling strategies, a brand-new era of 2D materials research could be developed.