Regulatory subunit of the cyclin-dependent kinase pair (CDK9/cyclin-T1) complex, also called positive transcription elongation factor B (P-TEFb), which is proposed to facilitate the transition from abortive to productive elongation by phosphorylating the CTD (C-terminal domain) of the large subunit of RNA polymerase II (RNA Pol II). (Microbial infection) In case of HIV or SIV infections, binds to the transactivation domain of the viral nuclear transcriptional activator, Tat, thereby increasing Tat's affinity for the transactivating response RNA element (TAR RNA). Serves as an essential cofactor for Tat, by promoting RNA Pol II activation, allowing transcription of viral genes. Cyclin-T1 is the predominant cyclin that associates with CDK9 to form a heterodimer called P-TEFb. P-TEFb forms a complex with AFF4/AF5Q31. Component of a complex which is at least composed of HTATSF1/Tat-SF1, P-TEFb complex, RNA pol II, SUPT5H, and NCL/nucleolin (PubMed:10393184). Component of the 7SK snRNP complex at least composed of P-TEFb (composed of CDK9 and CCNT1/cyclin-T1), HEXIM1, HEXIM2, BCDIN3, SART3 proteins and 7SK and U6 snRNAs (PubMed:17643375). Interacts with BRD4, targets chromatin binding (PubMed:16109376, PubMed:16109377, PubMed:24360279). Interacts with JMJD6 (PubMed:24360279). Interacts with MDFIC (PubMed:12944466). Interacts with HSF1 (PubMed:27189267). Interacts with HTATSF1 (PubMed:10913173). Interacts with AFF4 (PubMed:12065898). Interacts with TBX21 (PubMed:27292648). (Microbial infection) Interacts with the transactivation region of HIV-1, HIV-2 and SIV Tat. Ubiquitously expressed. Interaction between Tat and cyclin-T1 requires zinc. Belongs to the cyclin family. Cyclin C subfamily.