We study conjunctive queries with unequalities (x ≠ y) and we identify cases when query containment can still be characterized by the existence of homomorphisms. We also identify a class of GLAV-like database schema mappings with unequalities, for which the chase theorem holds, and thus data exchange has the same complexity as for GLAV mappings. Finally, we define a notion of consistency and provide an algorithm to check whether a set of mappings is consistent.