Abstract Database processing subsumes a variety of algorithmic activities that must be performed in modern database management systems. These mostly stem from the specific functionality provided by a database system to applications at various levels. We divide this functionality into two major layers. At the application layer , a database system has to process queries . To this end, we describe how query processing and optimization take places in relational database systems. For a subclass of relational queries we discuss optimization, and for the most important relational operation, the (natural) join , we sketch algorithms for its internal implementation. At the system layer , user requests to a database are treated in terms of transactions , which are atomic units of work that preserve database consistency. Transaction processing amounts to interleaved and resilient executions of multiple database accesses according to predefined goals. We explain the major techniques exploited here and show how they carry over to distributed database servers. We conclude by mentioning current and future challenges to database processing. Functional Layers in Database Systems Relational Databases Transaction Management Distributed Database Servers Future Challenges