State-of-the-art deep neural network recognition systems are designed for a static and closed world. It is usually assumed that the distribution at test time will be the same as the distribution during training. As a result, classifiers are forced to categorise observations into one out of a set of predefined semantic classes. Robotic problems are dynamic and open world; a robot will likely observe objects that are from outside of the training set distribution. Classifier outputs in robotic applications can lead to real-world robotic action and as such, a practical recognition system should not silently fail by confidently misclassifying novel observations. We show how a deep metric learning classification system can be applied to such open set recognition problems, allowing the classifier to label novel observations as unknown. Further to detecting novel examples, we propose an open set active learning approach that allows a robot to efficiently query a user about unknown observations. Our approach enables a robot to improve its understanding of the true distribution of data in the environment, from a small number of label queries. Experimental results show that our approach significantly outperforms comparable methods in both the open set recognition and active learning problems.