The design of adaptive model predictive controllers that rely on discrete time, stochastic, linear models, are described. In order to compute the manipulated variable, a quadratic cost is minimized in a receding horizon sense. The fact that hard inequality constraints are not imposed, allows to express the control law in closed form, either as a feedback from a nonminimum plant state made of input/output samples or a discrete transfer function. The adaptation mechanism consists of the estimation of model parameters using recursive least squares, together with the assumption of the certainty equivalence principle. Different assumptions of the manipulated variable over the optimization horizon lead to different basic models and lead to the GPC and MUSMAR control algorithms. Modifications of the basic algorithms to include constraints on the mean-square value of the manipulated variable and to avoid adaptation transients, based on an approximate solution of the so-called dual problem are addressed. Experimental results on distributed collector solar fields as well as on plants with similar dynamics (such as superheated steam on a boiler and arc welding) are described, providing practical examples that serve as a guideline to configure the controllers.