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This paper gives an overview on the theoretical results of recently developed algorithms for iterative controller tuning based on the correlation approach. The basic idea is to decorrelate the output error between the achieved and designed closed-loop systems by iteratively tuning the controller parameters. Two different approaches are investigated. In the first one, a correlation equation involving a vector of instrumental variables is solved using the stochastic approximation method. It is shown that, with an appropriate choice of instrumental variables and a finite number of data at each iteration, the algorithm converges to the solution of the correlation equation. The convergence conditions are derived and the accuracy of the estimates are studied. The second approach is based on the minimization of a correlation criterion. The frequency analysis of the criterion shows that the two norm of the error between the desired and achieved closed-loop transfer functions is minimized independently of the noise characteristics. This analysis leads to the definition of a generalized correlation criterion which allows the mixed sensitivity problem to be handled in two norm.