<p>Extracting earthquake precursors from observation data is a long-standing challenge. In principle, the observation data are the first-hand information to understand the earthquake process, and anomaly extraction is a necessary step to discover earthquake precursors, as well as hopefully enable earthquake prediction. At present, advancements in monitoring systems and anomaly extraction technologies have improved our understanding of many earthquake cases. However, due to diverse geophysical measurement techniques, as well as there could be some different theories and consequent signals induced by earthquake activity, anomaly extraction techniques remain fragmented, with no unified technological consensus established. This review uniquely summarizes time-series-based anomaly extraction techniques across geophysical observations for earthquake precursors, unlike existing reviews that mainly concentrate on individual geophysical observation types. Specifically, we outline the classification of anomaly extraction techniques in time-series observations by investigating their data types, the associated anomaly types, and the corresponding extraction methods. It is found that the growing data and precursor knowledge have shifted extraction methods from traditional to data-driven approaches, transforming anomalies into complex contextual or pattern signals preceding earthquakes. This review offers a practical reference framework for assessing extraction techniques and refining their performance in terms of data and anomaly types. We also hope this investigation will advance understanding of evolving extraction methods and their predictive potential.</p>