By temporarily deferring the repair of DNA lesions encountered during replication, the bypass of DNA damage is critical to the ability of cells to withstand genomic insults. Damage bypass can be achieved either by recombinational mechanisms that are generally accurate or by a process called translesion synthesis. Translesion synthesis involves replacing the stalled replicative polymerase with one of a number of specialized DNA polymerases whose active sites are able to tolerate a distorted or damaged DNA template. While this property allows the translesion polymerases to synthesize across damaged bases, it does so with the trade-off of an increased mutation rate. The deployment of these enzymes must therefore be carefully regulated. In addition to their important role in general DNA damage tolerance and mutagenesis, the translesion polymerases play a crucial role in converting the products of activation induced deaminase-catalysed cytidine deamination to mutations during immunoglobulin gene somatic hypermutation. In this paper, we specifically consider the control of translesion synthesis in the context of the timing of lesion bypass relative to replication fork progression and arrest at sites of DNA damage. We then examine how recent observations concerning the control of translesion synthesis might help refine our view of the mechanisms of immunoglobulin gene somatic hypermutation.