Abstract: Ontologies proliferate with the growth of the semantic Web. To date, however, most of the data on the Web are still stored in relational databases. Therefore, it is important to establish interoperability between relational databases and ontologies for creating a Web of data. An effective way to achieve such interoperability is to discover mappings between relational database schemas and ontologies. In this paper, some definitions in terms of mapping between a relational database schema and an ontology are firstly presented, and two major difficulties are analyzed from the standpoints of model construction and concrete application context. Then, a large number of popular existing solutions are surveyed according to three different facets, i.e., the approaches of model transformation (e.g., transforming ontologies to relational database schemas, transforming relational database schemas to ontologies, or transforming both relational database schemas and ontologies to medium models), the scopes of mapping strategies (e.g., automatization, and number of relational database schemas and ontologies), and the expressions of mapping results (e.g., simple correspondences, or semantic mappings). In addition, six representative mapping tools are introduced and compared with each other based on the three different facets mentioned above, and their unique features are highlighted in details. Finally, some remaining challenges are discussed, and some future research directions are also pointed out.