The problem of open-set recognition is considered. While previous approaches only consider this problem in the context of large-scale classifier training, we seek a unified solution for this and the low-shot classification setting. It is argued that the classic softmax classifier is a poor solution for open-set recognition, since it tends to overfit on the training classes. Randomization is then proposed as a solution to this problem. This suggests the use of meta-learning techniques, commonly used for few-shot classification, for the solution of open-set recognition. A new oPen sEt mEta LEaRning (PEELER) algorithm is then introduced. This combines the random selection of a set of novel classes per episode, a loss that maximizes the posterior entropy for examples of those classes, and a new metric learning formulation based on the Mahalanobis distance. Experimental results show that PEELER achieves state of the art open set recognition performance for both few-shot and large-scale recognition. On CIFAR and miniImageNet, it achieves substantial gains in seen/unseen class detection AUROC for a given seen-class classification accuracy.