Multistable mechanical metamaterials are a type of mechanical metamaterials with special features, such as reusability, energy storage and absorption capabilities, rapid deformation, and amplified output forces. These metamaterials are usually realized by series and/or parallel of bistable units. They can exhibit multiple stable configurations under external loads and can be switched reversely among each other, thereby realizing the reusability of mechanical metamaterials and offering broad engineering applications. This paper reviews the latest research progress in the design strategy, manufacture and application of multistable mechanical metamaterials. We divide bistable structures into three categories based on their basic element types and provide the criterion of their bistability. Various manufacturing techniques to fabricate these multistable mechanical metamaterials are introduced, including mold casting, cutting, folding and three-dimensional/4D printing. Furthermore, the prospects of multistable mechanical metamaterials for applications in soft driving, mechanical computing, energy absorption and wave controlling are discussed. Finally, this paper highlights possible challenges and opportunities for future investigations. The review aims to provide insights into the research and development of multistable mechanical metamaterials.