Complex object databases have been proposed as a significant extension of relational databases, with many practical applications. In the second database theory column, we present languages for the manipulation of such databases: a many-sorted algebra and an equivalent calculus. Without attempting to standardize, we try to provide general and short definitions that highlight the two key constructors of complex objects: tuples and (finite) sets. We comment on issues, such as language expressive power and complexity, and we describe equivalent rule-based languages with fixpoint semantics. Finally, we review the state-of-the art in database complex objects and list some interesting open questions.