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Anomaly detection algorithms are typically applied to static, unchanging, data features hand-crafted by the user. But how does a user systematically craft good features for anomalies that have never been seen? Here we couple deep learning with active learning -- in which an Oracle iteratively labels small amounts of data selected algorithmically over a series of rounds -- to automatically and dynamically improve the data features for efficient outlier detection. This approach, AHUNT, shows excellent performance on MNIST, CIFAR10, and Galaxy-DESI data, significantly outperforming both standard anomaly detection and active learning algorithms with static feature spaces. Beyond improved performance, AHUNT also allows the number of anomaly classes to grow organically in response to Oracle's evaluations. Extensive ablation studies explore the impact of Oracle question selection strategy and loss function on performance. We illustrate how the dynamic anomaly class taxonomy represents another step towards fully personalized rankings of different anomaly classes that reflect a user's interests, allowing the algorithm to learn to ignore statistically significant but uninteresting outliers (e.g., noise). This should prove useful in the era of massive astronomical datasets serving diverse sets of users who can only review a tiny subset of the incoming data.