Equivariant learning is a machine learning paradigm, where the symmetries of the unknown target function are encoded into the model class used to learn it. Examples include convolutional neural networks which respect translation symmetries, or graph neural networks which respect permutation symmetries. A symmetry-preserving model class is said to be universal if it can approximate all functions with the same symmetries. Many of the projects we are currently interested are related to the quest of devising efficient universal symmetry preserving architectures.