TFIIH is a 10-subunit RNA polymerase II basal transcription factor with a dual role in DNA repair. TFIIH contains three enzymatic functions and over 30 conserved subdomains and topological regions. We systematically tested the function of these regions in three TFIIH core module subunits, i.e., Ssl1, Tfb4, and Tfb2, in the DNA translocase subunit Ssl2, and in the kinase module subunit Tfb3. Our results are consistent with previously predicted roles for the Tfb2 Hub, Ssl2 Lock, and Tfb3 Latch regions, with mutations in these elements typically having severe defects in TFIIH subunit association. We also found unexpected roles for other domains whose function had not previously been defined. First, the Ssl1-Tfb4 Ring domains are important for TFIIH assembly. Second, the Tfb2 Hub and HEAT domains have an unexpected role in association with Tfb3. Third, the Tfb3 Ring domain is important for association with many other TFIIH subunits. Fourth, a partial deletion of the Ssl1 N-terminal extension (NTE) domain inhibits TFIIH function without affecting subunit association. Finally, we used site-specific cross-linking to localize the Tfb3-binding surface on the Rad3 Arch domain. Our cross-linking results suggest that Tfb3 and Rad3 have an unusual interface, with Tfb3 binding on two opposite faces of the Arch.