We investigate the computational complexity of reasoning over various fragments of the Extended Entity-Relationship (EER) language, which includes a number of constructs: ISA between entities and relationships, disjointness and covering of entities and relationships, cardinality constraints for entities in relationships and their refinements as well as multiplicity constraints for attributes. We extend the known EXPTIME-completeness result for UML class diagrams  and show that reasoning over EER diagrams with ISA between relationships is EXPTIME-complete even without relationship covering. Surprisingly, reasoning becomes NP-complete when we drop ISA between relationships (while still allowing all types of constraints on entities). If we further omit disjointness and covering over entities, reasoning becomes polynomial. Our lower complexity bound results are proved by direct reductions, while the upper bounds follow from the correspondences with expressive variants of the description logic DL-Lite, which we establish in this paper. These correspondences also show the usefulness of DL-Lite as a language for reasoning over conceptual models and ontologies.