This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control. This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, which has achieved an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.