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Summary form only given. The problem of streaming data has gained importance in recent years because of advances in hardware technology. The ubiquitous presence of data streams in a number of practical domains has generated a lot of research in this area. Example applications include surveillance for terrorist attack, network monitoring for intrusion detection, and others. Problems such as data mining which have been widely studied for traditional data sets cannot be easily solved for the data stream domain. This is because the large volume of data arriving in a stream renders most algorithms to inefficient as most mining algorithms require multiple scans of data which is unrealistic for stream data. More importantly, the characteristics of the data stream can change over time and the evolving pattern needs to be captured. Furthermore, we also need to consider the problem of resource allocation in mining data streams. Due to the large volume and the high speed of streaming data, mining algorithms must cope with the effects of system overload. Thus, how to achieve optimum results under various resource constraints becomes a challenging task. In this talk, the author provides an overview, discusses the issues and focuses on how to mine evolving data streams and perform resource adaptive computation.