Given a huge, online stream of time-evolving events with multiple attributes, such as online shopping logs: (item, price, brand, time), how can we summarize large, dynamic high-order tensor streams? How can we see any hidden patterns, rules, and anomalies? Our answer is to focus on two types of patterns, i.e., "regimes" and "components", over high-order tensor streams, for which we present an efficient and effective method, namely CubeScope. Specifically, it identifies any sudden discontinuity and recognizes distinct dynamical patterns, "regimes" (e.g., weekday/weekend/holiday patterns).In each regime, it also performs multi-way summarization for all attributes (e.g., item, price, brand, and time) and discovers hidden "components" representing latent groups (e.g., item/brand groups) and their relationship. Thanks to its concise but effective summarization, CubeScope can also detect the sudden appearance of anomalies and identify the types of anomalies that occur in practice.Our proposed method has the following properties: (a) Effective: it captures dynamical multi-aspect patterns, i.e., regimes and components, and statistically summarizes all the events; (b) General: it is practical for successful application to data compression, pattern discovery, and anomaly detection on various types of tensor streams; (c) Scalable: our algorithm does not depend on the length of the data stream and its dimensionality. Extensive experiments on real datasets demonstrate that CubeScope finds meaningful patterns and anomalies correctly, and consistently outperforms the state-of-the-art methods as regards accuracy and execution speed.