Title: Open-world Semi-supervised Learning. Abstract: Supervised and semi-supervised learning methods have been traditionally designed for the closed-world setting which is based on the assumption that unlabeled test data contains only classes previously encountered in the labeled training data. However, the real world is often open and dynamic, and thus novel previously unseen classes may appear in the test data or during the model deployment. Here, we introduce a new open-world semi-supervised learning setting in which the model is required to recognize previously seen classes, as well as to discover novel classes never seen in the labeled dataset. To tackle the problem, we propose ORCA, an approach that jointly learns a feature representation and a classifier on the labeled and unlabeled subsets of the data. The key idea in ORCA is in introducing uncertainty based adaptive margin that effectively circumvents the bias caused by the imbalance of variance between seen and novel classes. We demonstrate that ORCA accurately discovers novel classes and assigns samples to previously seen classes on standard benchmark image classification datasets, including  CIFAR and ImageNet. Remarkably, despite solving the harder task ORCA outperforms semi-supervised methods on seen classes, as well as novel class discovery methods on unseen classes, achieving 7% and 151% improvements on seen and unseen classes of the ImageNet dataset.