In recent years, active magnetic bearing systems (AMBs) have attracted the attention of researchers as suitable replacements for conventional mechanical and hydrostatic bearings. The absence of mechanical frictions, high-precision and low maintenance costs have all made AMBs suitable technologies for high-speed and high-precision applications. However, along with the numerous advantages, several challenges have hindered the widespread applications of these systems. AMBs are inherently open-loop unstable and hence feedback controllers are essential for stabilisation of AMB equipped systems. The multiple-input multiple-output nature of AMBs and the presence of high-frequency resonant modes further exacerbate the problem of modelling and control design of such systems.