Real-world use of RDF requires the ability to transparently represent and explain metadata associated with RDF triples. For example, when RDF triples are extracted automatically by information extraction programs, there is a need to represent where the triples came from, what their temporal validity is, and how certain we are that the triple is correct. Today, there is no theoretically clean and practically scalable mechanism that spans these different needs - reification is the only solution propose to date, and its implementations have been ugly. In this paper, we present Annotated RDF (or aRDF for short) in which RDF triples are annotated by members of a partially ordered set (with bottom element) that can be selected in any way desired by the user. We present a formal declarative semantics (model theory) for annotated RDF and develop algorithms to check consistency of aRDF theories and to answer queries to aRDF theories. We show that annotated RDF supports users who need to think about the uncertainty, temporal aspects, and provenance of the RDF triples in an RDF database. We develop a prototype aRDF implementation and show that our algorithms work efficiently even on real world data sets containing over 10 million triples.