An overview is presented of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering. Both the equation-error and output-error formulations are described, although the focus is on the adaptive algorithms and properties of the output-error configuration. These parameter-update algorithms have the same generic form, and they are based on a prediction-error performance criterion. A direct-form implementation of the adaptive filters is emphasized, but alternative realizations such as the parallel and lattice forms are briefly discussed. Several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence, are addressed.< >