The performance of vibration isolation mounts in reducing transmission of vibrations from a machine to the large structure on which the machine is mounted is considered. The trade-offs between relative displacement, machine acceleration and structure acceleration that limit the performance of passive isolation systems are well known. Active isolation systems are also shown to suffer from some fundamental performance limitations due to the presence of invariant points. Two standard configurations - disturbance input being a force and disturbance input being a displacement - are considered. In each case, the presence of invariant points in the relative deflection and acceleration transfer functions limits the performance that can be obtained. In the case of the standard force disturbance configuration, an invariant point is shown to occur at the structural resonant frequency. In the case of the displacement disturbance input, the invariant points do not coincide with any resonant frequency and therefore good broadband performance can be obtained. An active control law that optimizes a quadratic performance index is obtained for this case. A semi-active version of the control law is implemented on a vibration test rig using a magneto-rheological fluid damper as an actuator. Experimental results confirm the predicted performance characteristics of the semi-active vibration isolation system.