Faithful replication of DNA is a critical aspect in maintaining genome integrity. DNA polymerases are responsible for replicating DNA, and high-fidelity polymerases do this rapidly and at low error rates. Upon exposure to exogenous or endogenous substances, DNA can become damaged and this can alter the speed and fidelity of a DNA polymerase. In this instance, DNA polymerases are confronted with an obstacle that can result in genomic instability during replication, for example, by nucleotide misinsertion or replication fork collapse. It is important to know how DNA polymerases respond to damaged DNA substrates to understand the mechanism of mutagenesis and chemical carcinogenesis. Single-molecule techniques have helped to improve our current understanding of DNA polymerase-mediated DNA replication, as they enable the dissection of mechanistic details that can otherwise be lost in ensemble-averaged experiments. These techniques have also been used to gain a deeper understanding of how single DNA polymerases behave at the site of the damage in a DNA substrate. In this review, we evaluate single-molecule studies that have examined the interaction between DNA polymerases and damaged sites on a DNA template.