Ontology-based Data Access (OBDA) is gaining importance both scientifically and practically. However, little attention has been paid so far to the problem of updating OBDA systems. This is an essential issue if we want to be able to cope with modifications of data both at the ontology and at the source level, while maintaining the independence of the data sources. In this paper, we propose mechanisms to properly handle updates in this context. We show that updating data both at the ontology and source level is first-order rewritable. We also provide a practical implementation of such updating mechanisms based on non-recursive Datalog