Active Magnetic Bearings (AMB) are becoming increasingly significant for various industrial applications. Examples are turbo-compressors, centrifuges, high speed milling and grinding spindles, vibration isolation, linear guides, magnetically levitated trains, vacuum and space applications. Thanks to the rapid progress and drastic cost reduction in power- and micro-electronics, the number of AMB applications is growing very rapidly. Industrial uses of AMBs leads to new requirements for AMB-actuators, sensor systems, and rotor dynamics. Especially desirable are new and better control concepts to meet demand such as low cost AMB, high stiffness, high performance, high robustness, high damping up to several kHz, vibration isolation, force-free rotation, and unbalance cancellation. This paper surveys various control concepts for AMBs and discusses their advantages and disadvantages. Theoretical and experimental results are presented.