Genomes of all living organisms are constantly injured by endogenous and exogenous agents that modify the chemical integrity of DNA and in turn challenge its informational content. Despite the efficient action of numerous repair systems that remove lesions in DNA in an error-free manner, some lesions, that escape these repair mechanisms, are present when DNA is being replicated. Although replicative DNA polymerases are usually unable to copy past such lesions, it was recently discovered that cells are equipped with specialized DNA polymerases that will assist the replicative polymerase during the process of Translesion Synthesis (TLS). These TLS polymerases exhibit relaxed fidelity that allows them to copy past lesions in DNA with an inherent risk of generating mutations at high frequency. We present recent aspects related to the genetics and biochemistry of TLS and highlight some of the remaining hot topics of this field.