This article gives an overview of the theory and application of real-time control of accelerator beams. The design and structure of orbit feedbacks are described, going from basic local feedbacks to modern state-of-the art global systems. The time domain behaviour is analysed for the building blocks of the systems as well as from the spectrum of random sources driving the orbit perturbations. The use of predictive ltering is shown for the design of the control algorithm. A second important class is the control of tunes and chromaticities. Advanced tune measurements are performed using a digital phase-locked loop. The feedback systems are typically hybrid, simultaneously working on tune and coupling and chromaticity. Adaptive feed-forward algorithms are shown to be a suitable approach for use in energy ramping. For application in a high-speed bunch-by-bunch feedback system, ef cient low-noise data processing is presented for a digital lter. Also here, predictive ltering is shown to give well-adapted high-order lters
