3D reasoning capabilities are essential for physical intelligence and must therefore emerge in truly foundational robotics models. A conventional ML approach to acquiring 3D skills in robotics involves significantly augmenting 2D training data. In this approach, robots implicitly develop their 3D skills as a byproduct of generalizing across diverse scenes and conditions using 2D vision data. However scaling up training data for robotics is a challenge on its own. Another path is more explicit, using structural inductive biases and built-in architectural changes. This path leverages the rich 3D sensory input available to modern robots. In this talk, we will show some recent advances along this path to which members of the Google DeepMind Robot-Vision Team contributed. Those involve in particular 3D-aware attention mechanisms for Vision Transformers, which can be applied to various modalities (including depth images and point clouds) as well as new tools from Optimal Transport Theory for probabilistic distributions on 3D representations (e.g. meshes or point clouds).