In this paper we describe possible approaches how to store XML data, which is a key aspect for their further processing. One popular technique for managing XML data is to map the data to an existing database system, e.g., to the relational or object-relational database management system. We describe possible ways how to store XML data in relational databases, because relational systems are still widely used for various purposes, including XML data management. But XML data are trees, not tables, so the main focus of this article is oriented to native XML databases. We describe general properties of such kind of databases and, in particular, explain possible solutions on two experimental native XML database management systems – ExDB and CellStore. Both have been proposed, implemented and optimized in our research groups in recent years for experimental purposes.