Cancer cells display numerous abnormal characteristics which are initiated and maintained by elevated mutation rates and genome instability. Chromosomal DNA is continuously surveyed for the presence of damage or blocked replication forks by the DNA Damage Response (DDR) network. The DDR is complex and includes activation of cell cycle checkpoints, DNA repair, gene transcription, and induction of apoptosis. Duplicating a damaged genome is associated with elevated risks to fork collapse and genome instability. Therefore, the DNA damage tolerance (DDT) pathway is also employed to enhance survival and involves the recruitment of translesion DNA synthesis (TLS) polymerases to sites of replication fork blockade or single stranded DNA gaps left after the completion of replication in order to restore DNA to its double stranded form before mitosis. TLS polymerases are specialized for inserting nucleotides opposite DNA adducts, abasic sites, or DNA crosslinks. By definition, the DDT pathway is not involved in the actual repair of damaged DNA, but provides a mechanism to tolerate DNA lesions during replication thereby increasing survival and lessening the chance for genome instability. However this may be associated with increased mutagenesis. In this review, we will describe the specialized functions of Y family polymerases (Rev1, Polη, Polι and Polκ) and DNA polymerase ζ in lesion bypass, mutagenesis, and prevention of genome instability, the latter due to newly appreciated roles in DNA repair. The recently described role of the Fanconi anemia pathway in regulating Rev1 and Polζ-dependent TLS is also discussed in terms of their involvement in TLS, interstrand crosslink repair, and homologous recombination.