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Relational Keyword Search (R-KWS) provides an intuitive way to query relational data without requiring SQL, or knowledge of the underlying schema. In this article we describe a comprehensive framework for R-KWS covering snapshot queries on conventional tables and continuous queries on relational streams. Our contributions are summarized as follows: (i) We provide formal semantics, addressing the temporal validity and order of results, spanning uniformly over tables and streams; (ii) we investigate two general methodologies for query processing, graph based and operator based, that resolve several problems of previous approaches; and (iii) we develop a range of algorithms and optimizations covering both methodologies. We demonstrate the effectiveness of R-KWS, as well as the significant performance benefits of the proposed techniques, through extensive experiments with static and streaming datasets.