Abstract: 4D printing is an emerging technology that aims to endow objects produced by additive manufacturing with the ability to change shape or function over time. By converting planar precursor patterns into 3D structures with complex geometric shapes, 4D printing provides a flexible and efficient manufacturing method for the field. The design of the precursor structure is a crucial factor that affects the deformation effect of 4D printing. In this article, we aim to review the development of 4D printing based on strain mismatch from the perspective of precursor structure design. Firstly, we provided a brief overview of the current research situation on 4D printing. Then, we classified research related to structural design from the perspective of precursor structures in different dimensions, providing a comprehensive overview of 4D printing by different dimensions of precursor structures. Additionally, we discussed several auxiliary design methods for the precursor structure, including theoretical calculation models and simulation analysis to predict shape transformation, as well as reverse design tools to accurately design the precursor structure. Finally, we summarized and prospected the application prospects and challenges faced by 4D printing.