Abstract: Kirigami, an ancient art form originating from East Asian traditions, involves subtractive manufacturing or additive manufacturing through strategic cuts in a two-dimensional plane. Historically, kirigami has been used for decorative and ceremonial purposes, but it has evolved into a significant source of inspiration for modern engineering. These precise cuts not only enhance the material’s mechanical ductility but also enable transformative capabilities, allowing materials to shift from two-dimensional to three-dimensional configurations. This geometric manipulation facilitates controlled changes in stiffness, flexibility, and degrees of freedom at a mechanical level, making kirigami a versatile tool for engineering design. Based on the mechanical analysis method of compliant mechanisms, kirigami cuts can be categorized into two primary types: distributed compliance designs and lumped compliance designs. By meticulously engineering the compliance of these cuts, kirigami structures can achieve multistability, thereby enabling functionalities such as reconfigurability, variable cellular structures, self-assembly, and self-locking. As a result, multistable kirigami constitutes a multidisciplinary research area requiring multi-dimensional design approaches that draw upon knowledge from solid mechanics, mechanism science, artificial intelligence, and metamaterials. Its applications are vast and diverse; spanning fields such as space-expandable structures, flexible electronics, soft robotics, and micro/nano devices. This paper provides a comprehensive review of typical design methodologies for multistable kirigami by elucidating the underlying principles of mechanics and compliant mechanisms while summarizing the common geometric topologies of multistable kirigami structures. It also introduces the kirigami-based mechanical metamaterials and highlights the role of machine learning in the inverse design of their mechanical properties. Machine learning algorithms can optimize the geometric parameters of kirigami cuts to achieve desired mechanical behaviors, such as specific force-displacement responses or configurations. Furthermore, the paper concludes with an exploration of the design extensions of kirigami-inspired intelligent devices and provides an outlook on future development trends, aiming to propose novel ideas to improve the design and broaden the applications of multistable kirigami.