Many endogenous and exogenous factors can induce genomic instability in human cells, in the form of DNA damage and mutations, that predispose them to cancer development. Normal cells rely on DNA damage bypass pathways such as translesion synthesis (TLS) and template switching (TS) to replicate past lesions that might otherwise result in prolonged replication stress and lethal double-strand breaks (DSBs). However, due to the lower fidelity of the specialized polymerases involved in TLS, the activation and suppression of these pathways must be tightly regulated by post-translational modifications such as ubiquitination in order to limit the risk of mutagenesis. Many cancer cells rely on the deregulation of DNA damage bypass to promote carcinogenesis and tumor formation, often giving them heightened resistance to DNA damage from chemotherapeutic agents. In this review, we discuss the key functions of ubiquitin and ubiquitin-like proteins in regulating DNA damage bypass in human cells, and highlight ways in which these processes are both deregulated in cancer progression and might be targeted in cancer therapy.