This paper studies summarizing key information from news streams. We propose simple yet effective models to solve the problem based on a novel and promising representation of text streams -- Burst Information Networks (BINets). A BINet can be aware of redundant information, allows global analysis of a text stream, and can be efficiently built and dynamically updated, which perfectly fits the demands of text stream summarization. Extensive experiments show that the BINet-based approaches are not only efficient and can be used in a real-time online summarization setting, but also can generate high-quality summaries, outperforming the state-of-the-art approach.