We formally define the constraint database model, the concept of query in this model, and the basic constraint query languages provided by the relational calculus, the relational algebra, and DATALOG. We show how a computationally complete constraint query language can be obtained by augmenting the constraint relational calculus with basic programming language features. We look into some basic model-theoretic issues concerning the constraint relational calculus, in particular the equivalence problem. The notion of o-minimal structure turns out to be a useful abstraction to discuss these issues in some generality. We will see that equivalence of relational calculus queries on constraint databases is typically undecidable, but that it is decidable in the special case of conjunctive queries on constraint databases.