Three-dimensional (3D) printing is a new paradigm in customized manufacturing and allows the fabrication of complex structures that are difficult to realize with other conventional methods. Four-dimensional (4D) printing adds active, responsive functions to 3D-printed components, which can respond to various environmental stimuli. This review introduces recent ideas in 3D and 4D printing of mechanical multistable structures. Three-dimensional printing of multistable structures can enable highly reconfigurable components, which can bring many new breakthroughs to 3D printing. By adopting smart materials in multistable structures, more advanced functionalities and enhanced controllability can also be obtained in 4D printing. This could be useful for various smart and programmable actuators. In this review, we first introduce three representative approaches for 3D printing of multistable structures: strained layers, compliant mechanisms, and mechanical metamaterials. Then, we discuss 4D printing of multistable structures that can help overcome the limitation of conventional 4D printing research. Lastly, we conclude with future prospects.