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In this talk, I will discuss two recent works on how power-law anisotropy in the input data impact learning with non-linear models. In the first, based on https://arxiv.org/abs/2510.04780, I will discuss how data anisotropy impact the spectral properties of kernel methods, and how this translates (or not) to an improvement in their generalisation capacity. In the second, based on https://arxiv.org/abs/2511.18661, I will discuss the impact of power-law anisotropy on the convergence rate of gradient flow in the phase-retrieval setting, revealing a trade-off between weak and strong learning in this context.