Only a small fraction of the information on the Web is represented as Linked Data. This lack of coverage is partly due to the paradigms followed so far to extract Linked Data.While converting structured data to RDF is well supported by tools, most approaches to extract RDF from semi-structured data rely on extraction methods based on ad-hoc solutions. In this paper, we present a holistic and open-source framework for the extraction of RDF from templated websites. We discuss the architecture of the framework and the initial implementation of each of its components. In particular, we present a novel wrapper induction technique that does not require any human supervision to detect wrappers for web sites. Our framework also includes a consistency layer with which the data extracted by the wrappers can be checked for logical consistency. We evaluate the initial version of REX on three different datasets. Our results clearly show the potential of using templated Web pages to extend the Linked Data Cloud. Moreover, our results indicate the weaknesses of our current implementations and how they can be extended.