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Anomaly detection seeks to identify unusual phenomena, a central task in science and industry. The task is inherently unsupervised as anomalies are unexpected and unknown during training. Recent advances in self-supervised representation learning have directly driven improvements in anomaly detection. In this position paper, we first explain how self-supervised representations can be easily used to achieve state-of-the-art performance in commonly reported anomaly detection benchmarks. We then argue that tackling the next generation of anomaly detection tasks requires new technical and conceptual improvements in representation learning.