High-dimensional functions and operators arise throughout science and engineering, yet their approximation is hindered by the curse of dimensionality. Structured representations such as tensor networks, hierarchical decompositions, and compositional models (including feed-forward neural networks) can exploit the underlying structure. However, their practical performance depends critically on training sample selection, making active learning and optimal sampling essential for efficient approximation. This mini-symposium brings together researchers working on approximation theory, tensor methods, compositional models, and adaptive sampling to discuss recent advances in structured approximation and sample-efficient learning. Topics include sampling strategies, error estimates, anisotropic and hierarchical sparsity, and efficient algorithms for high-dimensional approximation.