The goal of this paper is to propose a coupling between the execution of a Image-Based Visual Servoing (IBVS) task and an active Structure from Motion (SfM) strategy. The core idea is to modify online the camera trajectory in the null-space of the (main) servoing task for rendering the camera motion 'more informative' w.r.t. the estimation of the 3-D structure. Consequently, the SfM convergence rate and accuracy is maximized during the servoing transient. The improved SfM performance also benefits the servoing execution, since a higher accuracy in the 3-D parameters involved in the interaction matrix improves the IBVS convergence by significantly mitigating the negative effects (instability, loss of feature visibility) of a poor knowledge of the scene structure. Active maximization of the SfM performance results, in general, in a deformed camera trajectory w.r.t. what would be obtained with a classical IBVS: therefore, we also propose an adaptive strategy able to automatically activate/deactivate the SfM optimization as a function of the current level of accuracy in the estimated 3-D structure. We finally report a thorough experimental validation of the overall approach under different conditions and case studies. The reported experiments support well the theoretical analysis and clearly show the benefits of the proposed coupling between visual control and active perception.