Microtubules have a key role in plant morphogenesis, as they control the oriented deposition of cellulose in the cell wall, and thus growth anisotropy. The idea that mechanical stress could be one of the main determinants behind the orientation of microtubules in plant cells emerged very soon after their discovery. The cause of mechanical stress in plant cells is turgor pressure, which can build up to 1 MPa and is restrained by cell wall stiffness. On the tissue scale, this can lead to regional patterns of tension, in particular in the epidermis of aerial organs, which resist the stress generated by cells in internal tissues. Here we summarize more than 50 years of work on the contribution of mechanical stress in guiding microtubule behavior, and the resulting impact on growth anisotropy and growth heterogeneity. We propose a conceptual model on microtubule dynamics and their ability to self-organize in bundles parallel to the direction of maximal stress, as well as a synthetic representation of the putative mechanotransducers at play.