Various combinatorial objects play a role in the representation theoryof symmetric groups, general linear groups and classical groups. Someclassical examples are partitions and Young tableaux which arise in therepresentation theory of symmetric groups. This talk will describeother combinatorial objects which arise in the representation theoryof finite classical groups via the work of Lusztig and others. More recentwork of Shoji and the speaker which makes connections between therepresentation theories of the finite general linear groups and ofsymplectic groups will also be described.