Optimal control relies on a model, which is generally uncertain because of incomplete knowledge of the system and changes in the dynamics over time. Probing the system under closed-loop control can reduce the model uncertainty through generating input-output data that is more informative than the data generated from normal operation. This paper addresses the problem of model predictive control (MPC) with active learning, with a particular focus on how incorporating probing in the control action can reduce model uncertainty. We discuss some of the central theoretical questions in this problem, and demonstrate the potential of active learning for maintaining MPC performance in the presence of uncertainty in model parameters and structure. Simulation results show that active learning is particularly beneficial when a system undergoes abrupt changes (such as the sudden occurrence of a fault) that can compromise operational safety, reliability, and profitability. (C) 2018 American Institute of Chemical Engineers