<p>The nonlinear energy sinks (NES) is a passive control device capable of achieving broadband vibration absorption. By utilizing targeted energy transfer mechanisms, NESs can effectively transfer and dissipate energy from the primary system, demonstrating great potential for engineering applications. However, due to their reliance on intrinsic nonlinear characteristics, the vibration reduction performance of NES is often limited to a specific range of external excitation intensities, which restricts their effectiveness under complex operating conditions. Multistable systems, which can switch between multiple stable equilibrium positions, offer unique advantages in energy conversion and response modulation. Introducing multistable mechanisms into NES is considered a promising strategy to enhance adaptability and broaden the effective vibration suppression range. This review summarizes the physical characteristics, modeling approaches, and typical response of multistable systems. Based on this foundation, it focuses on the application of multistable features in NES, including structural design, dynamic analysis, optimization, practical applications, and vibration suppression mechanisms. Furthermore, it presents a comparative analysis of the multistable NES, particularly in terms of adaptability to varying excitation intensities. The goal of this review is to provide researchers with a systematic knowledge framework and technical reference to support the advancement and practical implementation of multistable NES technologies.</p>