Several studies showed that in the sequence context 5′-C-Tg-purine, Tg is more likely to be bypassed by Klenow fragment, an A-family DNA polymerase. We set out to investigate the role of sequence context in Tg bypass in a B-family polymerase and to solve the crystal structures of the bacteriophage RB69 DNA polymerase in complex with Tg-containing DNA in the three remaining sequence contexts: 5′-A-Tg-G, 5′-T-Tg-G, and 5′-C-Tg-G. A combination of several factors—including the associated exonuclease activity, the nature of the 3′ and 5′ bases surrounding Tg, and the cis–trans interconversion of Tg—influences Tg bypass. We also visualized for the first time the structure of a well-ordered exonuclease complex, allowing us to identify and confirm the role of key residues (Phe123, Met256, and Tyr257) in strand separation and in the stabilization of the primer strand in the exonuclease site.