As intelligent computing systems, communication networks, and industrial infrastructure continue to expand in scale, time-series anomaly detection has become a key technology for improving system reliability. However, anomalies in real-world scenarios are often characterized by scarce labels, complex types, distribution drift, and difficulty of interpretation, making it hard for traditional detection methods to generalize reliably. Focusing on industrial time-series anomaly detection, we will introduce a systematic exploration of time-series anomaly detection: from unsupervised cross-domain adaptive detection to algorithm routing and expert fusion based on foundation models; from zero-shot anomaly detection using large-scale synthetic data to understandable anomaly explanations generated with large language models; and, further, the role of multimodal fusion of time series data, vision data, and text data in anomaly localization and semantic understanding.