###### Abstract  
This paper presents a comprehensive state-of-the-art review of magnetic negative stiffness (MNS) devices in the realm of vibration isolation systems, spanning from foundational theoretical models to practical engineering applications. The emergence of MNS technology represents a significant advancement in the field of vibration isolation, introducing a method capable of achieving near-zero stiffness to effectively attenuate low-frequency vibration. Through a systematic exploration of the evolution of vibration isolation methodologies--encompassing passive, active, and hybrid techniques--this article elucidates the underlying principles of quasi-zero stiffness (QZS) and investigates various configurations of MNS isolators, such as the linear spring, bending beam, level spring-link, and cam-roller designs. Our comprehensive analysis extends to the optimization and application of these isolators across diverse engineering domains, highlighting their pivotal role in enhancing the isolation efficiency against low-frequency vibrations. By integrating experimental validations with theoretical insights, this study underscores the transformative potential of MNS devices in redefining vibration isolation capabilities, particularly in expanding the isolation frequency band while preserving the load-bearing capacities. As the authors of this review, not only are the current advancements within MNS device research cataloged but also future trajectories are projected, advocating for continued innovation and tailored designs to fully exploit the advantages of MNS technology in specialized vibration isolation scenarios. MNS vibration isolation systems; quasi-zero stiffness; theoretical models; engineering applications; permanent magnet spring; electromagnetic spring +
Footnote †: journal: _Sci. shock absorbers, and acoustic insulation, the propagation of vibrations from both the interior and the exterior of the vehicle is significantly mitigated, yielding enhancements in passenger comfort and providing a quieter, smoother, and safer journey, while concurrently safeguarding vital vehicle components against potential damage [7; 8; 9]. In alternative contexts, even the most minute vibration may impinge upon the stealth capabilities of vessels and the operational efficiency of spacecraft [10; 11; 12]. Research into vibration isolation technology, particularly low-frequency isolation techniques, holds immense significance. Vibration isolation entails the suppression of vibrations in a controlled object by strategically isolating the vibration source through a dedicated system. In practical engineering applications, vibrations transmitted from the foundation to the equipment are primarily mitigated using vibration isolators [13]. A vibration isolator constitutes an elastic element that strategically connects equipment to a foundation. The primary function of a vibration isolator is to reduce or completely eliminate the transmission of vibrational forces between the foundation and the equipment. Classical vibration studies indicate that a linear vibration isolator can effectively attenuate vibrations exceeding the natural frequency of the isolation system by a specified multiplicative factor [14]. To effectively mitigate low-frequency vibrations, reducing the natural frequency of the isolation system is imperative. An effective strategy to accomplish this involves diminishing the stiffness of the isolation system [15]. However, this approach will result in increased displacement borne by the isolation system and a decreased load-bearing capacity. To address this challenge, QZS isolators have been developed in engineering practice. The progressive development of vibration isolation techniques has been motivated by the imperative to safeguard delicate equipment [16], enhance the comfort of transportation [17], and mitigate the adverse effects of vibrations on structural integrity [18]. Diverse methodologies have been devised over the course of time to meet these exigencies.