3D structures are crucial to biological function in the human body, driving interest in their in vitro fabrication. Advances in shape-morphing materials allow the assembly of 3D functional materials with the ability to modulate the architecture, flexibility, functionality, and other properties of the final product that suit the desired application. The principles of these techniques correspond to the principles of origami and kirigami, which enable the transformation of planar materials into 3D structures by folding, cutting, and twisting the 2D structure. In these approaches, materials responding to a certain stimulus will be used to manufacture a preliminary structure. Upon applying the stimuli, the architecture changes, which could be considered the fourth dimension in the manufacturing process. Here, we briefly summarize manufacturing techniques, such as lithography and 3D printing, that can be used in fabricating complex structures based on the aforementioned principles. We then discuss the common architectures that have been developed using these methods, which include but are not limited to gripping, rolling, and folding structures. Then, we describe the biomedical applications of these structures, such as sensors, scaffolds, and minimally invasive medical devices. Finally, we discuss challenges and future directions in using shape-morphing materials to develop biomimetic and bioinspired designs.