As a result of the extensive research in view-based query processing, three notions have been identified as fundamental, namely rewriting, answering, and losslessness. Answering amounts to computing the tuples satisfying the query in all databases consistent with the views. Rewriting consists in first reformulating the query in terms of the views and then evaluating the rewriting over the view extensions. Losslessness holds if we can answer the query by solely relying on the content of the views. While the mutual relationship between these three notions is easy to identify in the case of conjunctive queries, the terrain of notions gets considerably more complicated going beyond such a query class. In this paper, we revisit the notions of answering, rewriting, and losslessness and clarify their relationship in the setting of semistructured databases, and in particular for the basic query class in this setting, i.e., two-way regular path queries. Our first result is a clean explanation of the relationship between answering and rewriting, in which we characterize rewriting as a “linear approximation” of query answering. We show that applying this linear approximation to the constraint-satisfaction framework yields an elegant automata-theoretic approach to query rewriting. As for losslessness, we show that there are indeed two distinct interpretations for this notion, namely with respect to answering, and with respect to rewriting. We also show that the constraint-theoretic approach and the automata-theoretic approach can be combined to give algorithmic characterization of the various facets of losslessness. Finally, we deal with the problem of coping with loss, by considering mechanisms aimed at explaining lossiness to the user.