Variable stiffness vibration isolator (VSVI) can be switched between the low stiffness state and high stiffness state, respectively suitable for spacecraft requirement in cutting off the jitter transmitted from the bus to high accuracy payload and for avoiding long term adjustment during the process of attitude maneuver. For the advantage stated, the mechanism of VSVI is investigated for several types, considering the following factors: parallel manipulator with positive and negative stiffness components, structure with nonlinearity stiffness characteristics, smart materials or mechanisms, and maglev configuration. The design objectives of variable mechanisms are summarized into three indexes: adjustment range of stiffness, a lower limit of resonant frequency, and region with quasi-zero stiffness. Experimental studies for related isolators were presented, and the typical configuration or schematic diagram was shown under each index. As for the application of VSVI in spacecraft, research on the two significant problems, i.e. dynamic modeling and non-collocated control problem, is investigated for the design of control law of VSVI’s stiffness. Besides the complete description of spacecraft flexibility, variable stiffness characteristic that leads to a time-varying system and is easily coupled with the maneuvering process is worthy of more attention. Finally, challenges and future research are suggested for improving the performance in spacecraft application.