Various Earth anomalies have destroyed the stable, balanced state, resulting in fatalities and serious destruction of property. With the advantages of large-scale and precise observation, high-resolution remote sensing images have been widely used for anomaly monitoring and localization. Powered by the deep representation, the existing methods have achieved remarkable advances, primarily in classification and change detection techniques. However, labeled samples are difficult to acquire due to the low probability of anomaly occurrence, and the trained models are limited to fixed anomaly categories, which hinders the application for anomalies with few samples or unknown anomalies. In this paper, to tackle this problem, we propose the anomaly change detection (AnomalyCD) technique, which accepts time-series observations and learns to identify anomalous changes by learning from the historical normal change pattern. Compared to the existing techniques, AnomalyCD processes an unfixed number of time steps and can localize the various anomalies in a unified manner, without human supervision. To benchmark AnomalyCD, we constructed a high-resolution dataset with time-series images dedicated to various Earth anomalies (the AnomalyCDD dataset). AnomalyCDD contains high-resolution (from 0.15 to 2.39 m/pixel), time-series (from 3 to 7 time steps), and large-scale images (1927.93 km2 in total) collected globally Furthermore, we developed a zero-shot baseline model (AnomalyCDM), which implements the AnomalyCD technique by extracting a general representation from the segment anything model (SAM) and conducting temporal comparison to distinguish the anomalous changes from normal changes. AnomalyCDM is designed as a two-stage workflow to enhance the efficiency, and has the ability to process the unseen images directly, without retraining for each scene.