Data stream values are often associated with multiple aspects. For example, each value from environmental sensors may have an associated type (e.g., temperature, humidity, etc) as well as location. Aside from timestamp, type and location are the two additional aspects. How to model such streams? How to simultaneously find patterns within and across the multiple aspects? How to do it incrementally in a streaming fashion? In this paper, all these problems are addressed through a general data model, tensor streams, and an effective algorithmic framework, window-based tensor analysis (WTA). Two variations of WTA, independentwindow tensor analysis (TW) and moving-window tensor analysis (MW), are presented and evaluated extensively on real datasets. Finally, we illustrate one important application, Multi-Aspect Correlation Analysis (MACA), which uses WTA and we demonstrate its effectiveness on an environmental monitoring application.