Abstract : While the data deluge accelerates, most of the data produced remains locked in deep Web databases. For the linked open data to benefit from the potential represented by this huge amount of data, it is crucial to come up with solutions to expose heterogeneous databases as linked data. The xR2RML mapping language is an endeavor towards this goal: it is designed to map various types of databases to RDF, by flexibly adapting to heterogeneous query languages and data models while remaining free from any specific language. It extends R2RML, the W3C recommendation for the mapping of relational databases to RDF, and relies on RML for the handling of various data formats. In this paper we present xR2RML, we analyse data models of several modern databases as well as the format in which query results are returned , and we show how xR2RML translates any result data element into RDF, relying on existing languages such as XPath and JSONPath when necessary. We illustrate some features of xR2RML such as the generation of RDF collections and containers, and the ability to deal with mixed data formats. We also describe a real-world use case in which we applied xR2RML to build a SKOS thesaurus aimed at supporting studies on History of Zoology, Archaeozoology and Conservation Biology.