We consider the problem of construction of optimal experimental designs for linear regression models with correlated observations. In the first part of the talk, we assume that the ordinary least square estimator is used. The approach of Bickel-Herzberg is reviewed and several generalization of this approach are discussed. Then we consider the problem of construction of BLUE and some of its discrete approximations. In this case, the problem of construction of asymptotically optimal experimental designs is much more evolved. The celebrated Sacks-Ylvisaker approach is reviewed and several approximate methods of construction of optimal estimators and designs are discussed.