View-based query answering is the problem of answering a query based only on the answers precomputed for a set of views. While this problem has been widely investigated in databases, it is largely unexplored in the context of Description Logic ontologies. Differently from traditional databases, Description Logics may express several forms of incomplete information, and this poses challenging problems in characterizing the semantics of views. In this paper, we first present a general framework for view-based query answering, where we address the above semantical problems by defining a spectrum of notions of view-based query answering over ontologies, all based on the idea that the precomputed answers to views are the certain answers to the corresponding queries. We also relate such notions to relevant issues in ontology management, in particular ontology access authorization. Then, we provide decidability results, algorithms, and data complexity characterizations for view-based query answering in several Description Logics, ranging from the DL-Lite family to very expressive Description Logics.