The quality of data is context dependent. Starting from this intuition and experience, we propose and develop a conceptual framework that captures in formal terms the notion of "context-dependent data quality". We start by proposing a generic and abstract notion of context, and also of its uses, in general and in data management in particular. On this basis, we investigate "data quality assessment" and "quality query answering" as context-dependent activities. A context for the assessment of a database D at hand is modeled as an external database schema, with possibly materialized or virtual data, and connections to external data sources. The database D is put in context via mappings to the contextual schema, which produces a collection C of alternative clean versions of D. The quality of D is measured in terms of its distance to C. The class C} is also used to define and do "quality query answering". The proposed model allows for natural extensions, like the use of data quality predicates, the optimization of the access by the context to external data sources, and also the representation of contexts by means of more expressive ontologies.