The Web of Data has become a reality over the past decade. But how do you browse all that data and how do you surf from one resource to the next by following the links in the datasets ? We will introduce the new CubicWeb, a Web Extension to make your favorite browser capable of handling RDF data so that you can surf the Semantic Web and chose how data is displayed and how you interact with it. The Web started as a set of linked documents written in HTML and displayed by hypertext browsers. With the dawn of the Web of data, the information exchanged between the server and the client can be encoded in a form that is directly machine processable instead of being embeded in text document for humans to interpret. We asked ourselves what would be a browser for the Web of data, that would not be limited to displaying documents and would allow its user to surf the gigantic graph of linked data by displaying each piece of data with the best visualization for the task at hand. With this goal in mind, we reinstanciated the ideas developed more than ten years ago for the user interface of the CubicWeb semantic web framework. The result is the CubicWeb Linked Data Browser, a Web Extension for the main browsers (Firefox et Chrome) that can turn into HTML the RDF data sent by servers, with the user choosing the best view among the ones she registered when configuring the extension. Nicolas Chauvat is the founder and CEO of Logilab, a company that has been since year 2000 at the forefront of the Semantic Web in France. Logilab created the CubicWeb framework and used it for many applications, including the high-profile data.bnf.fr and francearchives.fr.