While deep learning has been successfully applied to many tasks in computer graphics and vision, standard learning architectures often operate on shape representations that are dense and regular, like pixel or voxel grids. On the other hand, decades of computer graphics and geometry processing research have resulted in specialized algorithms and tools that use representations without such regular structure. In this thesis, we revisit conventional approaches in graphics in geometry to propose deep learning pipelines and inductive biases that are directly compatible with common geometry representations, without relying on simple uniform structure.Ph.D.