Learning from large amounts of unsupervised data and a small amount of supervision is an important open problem in computer vision. We propose a new semi-supervised learning method, Semantic Positives via Pseudo-Labels (SEMPPL), that combines labelled and unlabelled data to learn informative representations. Our method extends self-supervised contrastive learning—where representations are shaped by distinguishing whether two samples represent the same underlying datum (positives) or not (negatives)—with a novel approach to selecting positives. To enrich the set of positives, we leverage the few existing ground-truth labels to predict the missing ones through a k-nearest neighbors classifier by using the learned embeddings of the labelled data. We thus extend the set of positives with datapoints having the same pseudo-label and call these semantic positives. We jointly learn the representation and predict bootstrapped pseudo-labels. This creates a reinforcing cycle. Strong initial representations enable better pseudo-label predictions which then improve the selection of semantic positives and lead to even better representations. SEMPPL outperforms competing semi-supervised methods setting new state-of-the-art performance of 76% and 68.5% top-1accuracy when using a ResNet-50 and training on 10% and 1% of labels on ImageNet, respectively. Furthermore, when using selective kernels, SEMPPL significantly outperforms previous state-of-the-art achieving 72.3% and 78.3% top-1accuracy on ImageNet with 1% and 10% labels, respectively, which improves absolute +7.8% and +6.2% over previous work. SEMPPL also exhibits state-of-the-art performance over larger ResNet models as well as strong robustness, out-of-distribution and transfer performance. We release the checkpoints and the evaluation code at https://github.com/deepmind/semppl.