We present the ordinary Harish-Chandra theory for finite groups with a BN-pair in arbitrary non-defining characteristic and the relation to Hecke algebras. We then introduceLusztig induction for finite reductive groups, explain its basic properties, use it to define and investigate the duality operation on the character ring and the Steinberg character. In the final section we explain the d-Harish-Chandra theories for finite reductive groups which play a fundamenhtal role in modular representation theory of finite reductive groups.