Vast amounts of information is available in structured forms like spreadsheets, database relations, and tables found in documents and on the Web. We describe an approach that uses linked data to interpret such tables and associate their components with nodes in a reference linked data collection. Our proposed framework assigns a class (i.e. type) to table columns, links table cells to entities, and inferred relations between columns to properties. The resulting interpretation can be used to annotate tables, confirm existing facts in the linked data collection, and propose new facts to be added. Our implemented prototype uses DBpedia as the linked data collection and Wikitology for background knowledge. We evaluated its performance using a collection of tables from Google Squared, Wikipedia and the Web.