Web archiving is the process of collecting portions of the Web to ensure that the information is preserved for future exploitation. However, despite the increasing number of web archives worldwide, the absence of efficient and meaningful exploration methods still remains a major hurdle in the way of turning them into a usable and useful information source. In this paper, we focus on this problem and propose an RDF/S model and a distributed framework for building semantic profiles ("layers") that describe semantic information about the contents of web archives. A semantic layer allows describing metadata information about the archived documents, annotating them with useful semantic information (like entities, concepts and events), and publishing all this data on the Web as Linked Data. Such structured repositories offer advanced query and integration capabilities, and make web archives directly exploitable by other systems and tools. To demonstrate their query capabilities, we build and query semantic layers for three different types of web archives. An experimental evaluation showed that a semantic layer can answer information needs that existing keyword-based systems are not able to sufficiently satisfy.