Title: S3: Supervised Self-supervised Learning under Label Noise. Abstract: Despite the large progress in supervised learning with Neural Networks, there are significant challenges in obtaining high-quality, large-scale and accurately labeled datasets. In this context, in this paper we address the problem of classification in the presence of noisy labels and more specifically, both close-set and open-set label noise, that is when the true label of a sample may, or may not belong to the set of the given labels. In the heart of our method is a sample selection mechanism that relies on the consistency between the annotated label of a sample and the distribution of the labels in its neighborhood in the feature space, a relabeling mechanism that relies on the confidence of the classifier across subsequent iterations and a training strategy that trains the encoder both with a self-consistency loss and the classifier-encoder with cross-entropy loss on the selected samples alone. Without bells and whistles, such as co-training so as to reduce the self-confirmation bias, our method significantly surpasses previous methods on both CIFAR10/CIFAR100 with artificial noise and real-world noisy datasets such as WebVision and ANIMAL-10N.