The success of carbon nanotubes (CNTs) in increasing toughness of polymers and their composites is often attributed to the additional energy consumed by CNT debonding and pull out. In this work we demonstrate that this mechanism alone can only lead to modest improvements in toughness and that the true toughening power of CNTs lies in activation of multiple mechanisms. Our virtual experiments reveal three mechanisms: 1) suppression of stress concentrations leading to delay in damage initiation, 2) damage diffusion/crack branching and 3) CNT debonding and pull-out. The first two mechanisms dominate energy dissipation although they have received less attention in the literature. These mechanisms act concurrently at different scales and have complex dependence on the morphology of the CNT network and properties of the CNT/matrix interface. When CNTs' position, orientation and compatibility with polymer are optimised, the strength and toughness of the nanocomposite can be increased significantly (in the studied case by 90% and 277%, respectively, compared to unfilled polymer). Without morphological optimisation these improvements were only 6% and 14%, respectively. Thus, for strengthening and toughening of nanocomposite structures, it is insufficient to only modify the interface, one also needs to optimise CNTs’ spatial distribution and orientation.