This review focuses on eukaryotic translesion synthesis (TLS) DNA polymerases, and the emphasis is on Saccharomyces cerevisiae and human Y-family polymerases (Pols) eta, iota, kappa, and Rev1, as well as on Polzeta, which is a member of the B-family polymerases. The fidelity, mismatch extension ability, and lesion bypass efficiencies of these different polymerases are examined and evaluated in the context of their structures. One major conclusion is that, despite the overall similarity of basic structural features among the Y-family polymerases, there is a high degree of specificity in their lesion bypass properties. Some are able to bypass a particular DNA lesion, whereas others are efficient at only the insertion step or the extension step of lesion bypass. This functional divergence is related to the differences in their structures. Polzeta is a highly specialized polymerase specifically adapted for extending primer termini opposite from a diverse array of DNA lesions, and depending upon the DNA lesion, it contributes to lesion bypass in a mutagenic or in an error-free manner. Proliferating cell nuclear antigen (PCNA) provides the central scaffold to which TLS polymerases bind for access to the replication ensemble stalled at a lesion site, and Rad6-Rad18-dependent protein ubiquitination is important for polymerase exchange.