Anomaly detection (AD) aims to identify defective images and localize their defects (if any). Ideally, AD models should be able to detect defects over many image classes; without relying on hard-coded class names that can be uninformative or inconsistent across datasets; learn without anomaly supervision; and be robust to the long-tailed distributions of real-world applications. To address these challenges, we formulate the problem of long-tailed AD by introducing several datasets with different levels of class imbalance and metrics for performance evaluation. We then propose a novel method, LTAD, to detect defects from multiple and long-tailed classes, without relying on dataset class names. LTAD combines AD by reconstruction and semantic AD modules. AD by reconstruction is implemented with a transformer-based reconstruction module. Semantic AD is implemented with a binary classifier, which relies on learned pseudo class names and a pretrained foundation model. These modules are learned over two phases. Phase 1 learns the pseudo-class names and a variational autoencoder (VAE) for feature synthesis that augments the training data to combat long-tails. Phase 2 then learns the parameters of the reconstruction and classification modules of LTAD. Extensive experiments using the proposed long-tailed datasets show that LTAD substantially outperforms the state-of-the-art methods for most forms of dataset imbalance.