More and more human activities are supported by computerized systems. This generates more and more volumes of data to be considered when analysing and monitoring human activities. When the volume of data increases it becomes very expensive (sometimes impossible) to store all available data before processing them: it is necessary to process them 'on the fly' as streams of data. Moreover, many new applications generate directly streams of data produced by a large number of sensors (weather forecast, environmental studies, road traffic, health care, power plants, …). In order to face this increase of available data, much research work has been done in the USA to develop methods and tools to process on the fly streams of structured data (opposed to audio and video streams which are unstructured). A good survey of these approaches can be found in the recent Springer book of C.Aggarwal “Data Streams: Models and Applications”. Two main directions have been explored: (1) Data Stream Management Systems (DSMS) which enable to query streams 'on the fly', (2) data stream mining methods to apply data mining methods directly to the streams without storing them. The main characteristic of these approaches is that all the processing is done 'on the fly' without storing the entire streams. In order to achieve this goal, a common solution is to apply queries and data mining algorithms to a small part of the stream defined as a sliding window containing most recent information. In many applications, there is a need to keep an historical view of the streams, for instance to provide historical aggregate information from the streams or to detect anomalous behaviour of monitored systems. For these applications, applying queries and algorithms to sliding windows prevents from obtaining needed information: it is necessary to keep track of the history of the streams by building and updating summaries on the fly. The MIDAS project is a 'Recherche Fondamentale' project which aims at studying, developing and demonstrating new methods for summarizing data streams. It tackles the following scientific challenges related to the construction of summaries: 􀀹 Summaries are built from infinite streams but must have a fixed or low increasing size; 􀀹 The construction of summaries must be incremental (done 'on the fly'); 􀀹 The amount of CPU used to process each element of the streams must be compatible with the arrival rate of the elements; 􀀹 The summaries must cover the whole stream and enable to build summaries of any past part of the history of a stream. The MIDAS project gathers both academic and industrial partners. The academic partners are already active in the field of data stream management and mining. The industrial partners are very large companies (France Telecom and Electricité de France) who have to face the increase of available data to monitor their activity: they will provide problems and data to direct research and assess new developed approaches. The MIDAS project falls within the scope the 2nd thematic axis of the MDCO call: “Algorithms for processing massive data sets”.