TimeStream is a distributed system designed specifically for low-latency continuous processing of big streaming data on a large cluster of commodity machines. The unique characteristics of this emerging application domain have led to a significantly different design from the popular MapReduce-style batch data processing. In particular, we advocate a powerful new abstraction called resilient substitution that caters to the specific needs in this new computation model to handle failure recovery and dynamic reconfiguration in response to load changes. Several real-world applications running on our prototype have been shown to scale robustly with low latency while at the same time maintaining the simple and concise declarative programming model. TimeStream handles an on-line advertising aggregation pipeline at a rate of 700,000 URLs per second with a 2-second delay, while performing sentiment analysis of Twitter data at a peak rate close to 10,000 tweets per second, with approximately 2-second delay.