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In many application fields, such as production lines or stock analysis, it is substantial to create and process high amounts of data at high rates. Such continuous data flows with unknown size and end are also called data streams. The processing and analysis of data streams are a challenge for common data management systems as they have to operate and deliver results in real time. Data Stream Management Systems (DSMS), as an advancement of database management systems, have been implemented to deal with these issues. DSMS have to adapt to the notion of data streams on various levels, such as query languages, processing or optimization. In this chapter we give an overview of the basics of data streams, architecture principles of DSMS and the used query languages. Furthermore, we specifically detail data quality aspects in DSMS as these play an important role for various applications based on data streams. Finally, the chapter also includes a list of research and commercial DSMS and their key properties.