Conformal prediction is widely used to equip black-box machine learning models with uncertainty quantification enjoying formal coverage guarantees. However, these guarantees typically break down in the presence of distribution shifts, where the data distribution at test time differs from the training (or calibration-time) distribution. In this work, we address subpopulation shifts, where the test environment exhibits an unknown and differing mixture of subpopulations compared to the calibration data. We propose new methods that provably adapt conformal prediction to such shifts, ensuring valid coverage without requiring explicit knowledge of subpopulation structure. Our algorithms scale to high-dimensional settings and perform effectively in realistic machine learning tasks. Extensive experiments on vision (with vision transformers) and language (with large language models) benchmarks demonstrate that our methods reliably maintain coverage and controls risk in scenarios where standard conformal prediction fails.