Transfer learning is a standard technique to improve performance on tasks with limited data. However, for medical imaging, the value of transfer learning is less clear [38]. This is likely due to the large domain mismatch between the usual natural-image pre-training (e.g. ImageNet) and medical images. However, recent advances in transfer learning have shown substantial improvements from scale. We investigate whether modern methods can change the fortune of transfer learning for medical imaging. For this, we study the class of large-scale pre-trained networks presented by Kolesnikov et al. [23] on three diverse imaging tasks: chest radiography, mammography, and dermatology. We study both transfer performance and critical properties for the deployment in the medical domain, including: out-of-distribution generalization, data-efficiency, subgroup fairness, and uncertainty estimation. Interestingly, we find that for some of these properties, transfer from natural to medical images is indeed extremely effective, but only when performed at sufficient scale.