During S-phase, minor DNA damage may be overcome by DNA damage tolerance (DDT) pathways that bypass such obstacles, postponing repair of the offending damage to complete the cell cycle and maintain cell survival. In translesion DNA synthesis (TLS), specialized DNA polymerases replicate the damaged DNA, allowing stringent DNA synthesis by a replicative polymerase to resume beyond the offending damage. Dysregulation of this DDT pathway in human cells leads to increased mutation rates that may contribute to the onset of cancer. Furthermore, TLS affords human cancer cells the ability to counteract chemotherapeutic agents that elicit cell death by damaging DNA in actively replicating cells. Currently, it is unclear how this critical pathway unfolds, in particular, where and when TLS occurs on each template strand. Given the semidiscontinuous nature of DNA replication, it is likely that TLS on the leading and lagging strand templates is unique for each strand. Since the discovery of DDT in the late 1960s, most studies on TLS in eukaryotes have focused on DNA lesions resulting from ultraviolet (UV) radiation exposure. In this review, we revisit these and other related studies to dissect the step-by-step intricacies of this complex process, provide our current understanding of TLS on leading and lagging strand templates, and propose testable hypotheses to gain further insights.