Multistable composites, as a novel class of advanced composites, are characterized by two or more stable configurations that allow to remain in their respective equilibrium states without the continuous action of external loading. Owing to the advantages of lightweight, high mechanical strength, and good reconfigurability, multistable composite structures are widely used in aerospace industries, energy harvesters, robotic industries, etc. Such advanced composite structures have been extensively studied by means of theoretical analysis, experimental investigation, as well as finite element simulation. This holistic review provides recent advances in the reconfiguration mechanism, fabrication, and design of multistable composite structures. In addition, their applications in morphing structures, bioinspired structures, and soft robotics grippers are particularly highlighted with great potential in this promising field.