Abstract In this article define the concept of deductive database including the formal definition of a query and an answer to a query; we provide an historical background for deductive databases; we explain the different types of deductive databases starting with Datalog and including stratified, nonstratified, extended, and disjunctive deductive databases; we discuss various semantics for deductive databases; we list the prototypes and implementations of deductive databases; we also give several applications that cannot be handled by relational and databases and require deductive databases.