The demands on visual recognition systems do not end with the complexity offered by current large-scale image datasets, such as ImageNet. In consequence, we need curious and continuously learning algorithms that actively acquire knowledge about semantic concepts which are present in available unlabeled data. As a step towards this goal, we show how to perform continuous active learning and exploration, where an algorithm actively selects relevant batches of unlabeled examples for annotation. These examples could either belong to already known or to yet undiscovered classes. Our algorithm is based on a new generalization of the Expected Model Output Change principle for deep architectures and is especially tailored to deep neural networks. Furthermore, we show easy-to-implement approximations that yield efficient techniques for active selection. Empirical experiments show that our method outperforms currently used heuristics.