Regulation of the expression of the human immunodeficiency virus (HIV) genome is accomplished in large part by controlling transcription elongation. The viral protein Tat hijacks the host cell's RNA polymerase II elongation control machinery through interaction with the positive transcription elongation factor, P-TEFb, and directs the factor to promote productive elongation of HIV mRNA. Here we describe the crystal structure of the Tat.P-TEFb complex containing HIV-1 Tat, human Cdk9 (also known as CDK9), and human cyclin T1 (also known as CCNT1). Tat adopts a structure complementary to the surface of P-TEFb and makes extensive contacts, mainly with the cyclin T1 subunit of P-TEFb, but also with the T-loop of the Cdk9 subunit. The structure provides a plausible explanation for the tolerance of Tat to sequence variations at certain sites. Importantly, Tat induces significant conformational changes in P-TEFb. This finding lays a foundation for the design of compounds that would specifically inhibit the Tat.P-TEFb complex and block HIV replication.