Linked Data initiatives have fostered the publication of more than one thousand of datasets in the Linking Open Data (LOD) cloud from a large variety of domains, e.g., Life Sciences, Media, and Government. Albeit large in volume, Linked Data is essentially read-only and most collaborative tasks of cleaning, enriching, and reasoning are not dynamically available. Collaboration between data producers and consumers is essential for overcoming these limitations, and for fostering the evolution of the LOD cloud into a more participative and collaborative data space. In this paper, we describe the role that collaborative infrastructures can play in creating and maintaining Linked Data, and the benefits of exploiting knowledge represented in ontologies as well as the main features of Semantic Web technologies to effectively assess the LOD cloud's evolution. First, the advantages of using ontologies for modelling collaborative spaces are discussed, as well as formalisms for assessing semantic collaboration by sharing annotations from terms in domain ontologies. Then, Semantic MediaWiki communities are described, and illustrated with three applications in the domains of formal mathematics, ontology engineering, and pedagogical content management. Next, the problem of exploiting semantics in collaborative spaces is tackled, and three different approaches are described. Finally, we conclude with an outlook to future directions and problems that remain open in the area of semantically-driven collaborative spaces.